numerical method for solving stochastic differential equations with poissonian white shot noise we propose a numerical integration scheme to solve stochastic differential equations driven by poissonian white shot noise our formula which is based on an integral equation which is equivalent to the stochastic differential equation utilizes a discrete time approximation with fixed integration time step we show that our integration formula approaches the euler formula if the poissonian noise approaches the gaussian white noise the accuracy and efficiency of the proposed algorithm are examined by studying the dynamics of an overdamped particle driven by poissonian white shot noise in a spatially periodic potential we find that the accuracy of the proposed algorithm only weakly depends on the parameters characterizing the poissonian white shot noise this holds true even if the limit of gaussian white noise is approached

geometrical treatment of systems driven by coloured noise the authors use geometrical methods and functional derivative techniques to analyse the stochastic behaviour of multidegree of freedom nonlinear systems driven by gaussian noises with arbitrary correlation functions the method has the advantage of being also applicable to systems with an infinite number of degrees of freedom partial differential equations with some kind of hamiltonian structure and gives some insight into the nature of the approximations that lead to some of the main effective fokker planck equations used in the literature

lp metric sensitivity analysis for single and multi attribute decision analysis abstract analyzing the sensitivity of decisions to probability estimation error in single and multi attribute problems and to errors in estimating additive multi attribute value models in multi attribute problems is an integral part of decision analysis this paper presents an intuitive and tractable approach to this sensitivity analysis here a decision is considered insensitive if 1 the probabilities or multi attribute weights required for any other alternative to become preferred are not close to the original estimated probabilities and weights and 2 the rank order of states implied by the probabilities or the rank order of attributes implied by the additive multi attribute weights must change for any other alternative to become preferred the sensitivity analysis is conducted using straight forward linear programming models an example is used to demonstrate their application

passage time statistics in a stochastic verhulst model using the stochastic paths perturbation approach analytic individual realizations of a stochastic verhulst model are introduced the escape of the unstable state is studied for any kind of noise from these individual realizations we infer from these paths the statistics of the first passage time distribution invoking the solution of an explicit equation with a random coefficient a stochastic population verhulst s dynamics with small perturbations of the wiener class is explicitly worked out the method can also be implemented for other type of stochastic perturbations like poisson noise shot white pulses etc

linear systems with levy fluctuations abstract we have examined the response of multivariable linear systems to levy fluctuations the characteristic function of the response is obtained explicitly as a function of time using the characteristic function the fractional moments of the process are determined the nature of the product rule obeyed by the characteristic function of a general linear dynamical system is elucidated

brownian dynamics time averaging and colored noise we propose a method to obtain the equilibrium distribution for positions and velocities of a one dimensional particle via time averaging and laplace transformations we apply it to the case of a damped harmonic oscillator in contact with a thermal bath the present method allows us to treat among other cases a gaussian noise function exponentially correlated in time e g gaussian colored noise we obtain the exact equilibrium solution and study some of its properties

numerical solution of differential equations with colored noise using the general theory of numerical integration of stochastic differential equations a constructive approach to numerical methods for a system with colored noise is proposed efficient methods up to the 5 2 strong order and up to the third weak order including runge kutta and implicit schemes are presented the algorithms are tested on the kubo oscillator

uqosp 2 2 lattice models in this paper i construct lattice models with an underlying uqosp 2 2 superalgebra symmetry i find new solutions to the graded yang baxter equation these trigonometric r matrices depend on three continuous parameters the spectral parameter the deformation parameter q and the u 1 parameter b of the superalgebra it must be emphasized that the parameter q is generic and the parameter b does not correspond to the nilpotency parameter of the rational limits are given they also depend on the u 1 parameter and this dependence cannot be rescaled away i give the bethe ansatz solution of the lattice models built from some of these r matrices while for other matrices due to the particular nature of the representation theory of osp 2 2 i conjecture the result the parameter b appears as a continuous generalized spin finally i briefly discuss the problem of finding the ground state of these models

stochastic escape processes from a non symmetric potential normal form ii the marginal case the first passage time distribution to reach the attractor of the stochastic differential equation is analytically obtained by using a previously reported scheme the stochastic path perturbation approach a second order perturbation theory in the small noise parameter is introduced to analyse the random escape of the stochastic paths from the marginal unstable state x 0 the anomalous fluctuation of the phase space variable x t is analytically calculated by using the instanton like approximation we have carried out monte carlo simulations showing good agreement with our theoretical predictions

escape rates in periodically driven markov processes we present an approximate analytical expression for the escape rate of time dependent driven stochastic processes with an absorbing boundary such as the driven leaky integrateand fire model for neural spiking the novel approximation i s based on a discrete state markovian modeling of the full long time dynamics with time dependent rates it is valid in a wide parameter regime beyond the restraining limits of weak driving linear response and or weak noise the scheme is carefully tested and yields excellent agreement with three different numerical methods based on the langevin equation the fokker planck equation and an integral equation

a study on the action of non gaussian noise on a brownian particle abstract we analytically address the non equilibrium problem of a brownian particle in contact with a thermal reservoir by means of a non gaussian langevin noise term t the presence of noise kurtosis is akin to a second temperature reservoir acting on the system and we exploit its consequences by means of studying a converging exact form for the stationary probability distribution

persistent diffusion on a line we consider solutions to the telegraph equation describing persistent diffusion on a line under various initial conditions the first passage time distribution is evaluated in closed form biased persistent diffusion is also considered a direct derivation of the telegraph equation from the stochastic equation for the displacement is presented in an appendix

eigenvalues of casimir invariants for unitary irreps of a fully explicit formula for the eigenvalues of casimir invariants for u q gl m n is given which applies to all unitary irreps this is achieved by making some interesting observations on atypicality indices for irreps occurring in the tensor product of unitary irreps of the same type these results have applications in the determination of link polynomials arising from unitary irreps of u q gl m n

stochastic giant resonance the model of an electric circuit with dichotomous resistance is investigated it is shown that the dichotomous resistance can induce a phenomenon of stochastic giant resonance for the signal to noise ratio snr as a function of input signal frequency this phenomenon is a direct consequence of the existence of a zero noise power spectrum with a nonzero signal power spectrum for the same parameters in addition two kinds of the usual stochastic resonance phenomena have been obtained for the snr one is as a function of the correlation time of the asymmetric dichotomous resistance the other is as a function of the input signal frequency

twisted quantum affine superalgebra invariant r matrices and a new integrable electronic model we describe the twisted affine superalgebra sl 2 2 2 and its quantized version u q sl 2 2 2 we investigate the tensor product representation of the four dimensional grade star representation for the fixed point sub superalgebra u q osp 2 2 we work out the tensor product decomposition explicitly and find that the decomposition is not completely reducible associated with this four dimensional grade star representation we derive two u q osp 2 2 invariant r matrices one of them corresponds to u q sl 2 2 2 and the other to u q osp 2 2 1 using the r matrix for u q sl 2 2 2 we construct a new u q osp 2 2 invariant strongly correlated electronic model which is integrable in one dimension interestingly this model reduces in the q 1 limit to the one proposed by essler et al which has a larger sl 2 2 symmetry

on the relation between white shot noise gaussian white noise and the dichotomic markov process it is shown that the dichotomic markov process converges to a white shot noise interpreted according to the stratonovich integration rule in the joint limit in which the average duration of one of the states goes to zero and the value at this state goes to infinity a further limit procedure allows us to obtain gaussian white noise from white shot noise these results are applied to the problem of noise induced transitions it is shown that white shot noise can give rise to transitions which do not occur for gaussian white noise the above results are finally generalized in introducing compound dichotomic markov processes

novel types of sensitivity analysis for additive mcdm methods three novel types of sensitivity analysis are presented they determine the following 1 the sensitivity of a ranking to specific changes in the evaluations of all alternatives on certain criteria 2 the influence of specific changes in certain criterion scores of an alternative 3 the minimum modification of the weights required to make an alternative ranked first the use of these instruments is demonstrated by the results of a simulation experiment results show that the first and second type of sensitivity analysis enable to apply multiple criteria decision making mcdm methods in dynamic circumstances the third type of sensitivity analysis is demonstrated to be a tool to analyze the total weight space

fractional oscillator driven by a gaussian noise abstract the time dependent response is studied of a fractional oscillator driven by a gaussian white noise applying the method of characteristic functionals combined with the technique of integral transforms we derive explicit formulas for the variances of position and velocity and the asymptotic power spectrum of the oscillator the effects of the order of fractional derivative on statistical characteristics of the oscillator are analyzed numerically

generalized statistical mechanics connection with thermodynamics the authors show the manner through which the recent generalization by tsallis 1988 of the boltzmann gibbs statistics becomes consistent with a generalized thermodynamics preserving the legendre transformation framework of standard thermodynamics in addition to that they generalize the shannon additivity

nonextensive foundation of levy distributions a deep connection between the ubiquity of l evy distributions in nature and the nonextensive thermal statistics introduced a decade ago has been established recently tsallis et al phys rev lett 75 3589 1995 by using unnormalized q expectation values it has just been argued on physical grounds that normalized q expectation values should be used instead we revisit within this more appropriate scheme the l evy problem and verify that the relevant analytic results become sensibly simplified whereas the basic physics remains unchanged

the generalized wiener process ii finite systems a class of langevin like equations non markovian processes are studied in the presence of non natural boundary conditions exact results for all cumulants and the corresponding kolmogorov hierarchy of distributions are given in terms of our functional approach we previously reported 1997 j phys a math gen 30 8427 the generalized wiener processes on finite domains are completely characterized for reflecting and periodic boundary conditions some examples are given to show the behaviour of the moments and the probability distributions for different noises the interplay between the boundary conditions and the structure of the noises is also pointed out

solutions of the quantum yang baxter equation with extra nonadditive parameters we present a systematic technique to construct solutions to the yang baxter equation which depend not only on a spectral parameter but in addition on further continuous parameters these extra parameters enter the yang baxter equation in a similar way to the spectral parameter but in a non additive form we exploit the fact that quantum non compact algebras such as uq su 1 1 and type i quantum superalgebras such as uq gl 1 mod 1 and uq gl 2 mod 1 are known to admit non trivial one parameter families of infinite dimensional and finite dimensional irreps respectively even for generic q we develop a technique for constructing the corresponding spectral dependent r matrices as examples we work out the the r matrices for the three quantum algebras mentioned above in certain representations

sensitivity analysis of additive multiattribute value models we present two simple computational procedures for sensitivity analysis of additive multiattribute value models that yield variations in attribute weights scaling constants for the first or entropy based procedure the point of departure is the concept of equal weights for all attributes for the second or least squares procedure the point of departure is a set of arbitrary weights for attributes in each procedure we either a calculate the closest set of weights that equates the multiattribute value for a pair of alternatives that alternative whose overall value is optimal for the original attribute weights and any other specific nondominated alternative or b calculate the closest set of weights required for the specific alternative to exceed the optimal alternative by a specified amount

the rigid rotator with levy noise abstract we have used an exact functional approach to solve a plane rotator in presence of levy noise the cosine relaxation has been calculated its non autonomous generalization can also be solved in the context of our functional analysis

response to a periodic stimulus in a perfect integrate and fire neuron model driven by colored noise the output interspike interval statistics of a stochastic perfect integrate and fire neuron model driven by an additive exogenous periodic stimulus is considered the effect of temporally correlated random activity of synaptic inputs is modeled by an additive symmetric dichotomous noise using a first passage time formulation exact expressions for the output interspike interval density and for the serial correlation coefficient are derived in the nonsteady regime and their dependence on input parameters e g the noise correlation time and amplitude as well as the frequency of an input current is analyzed it is shown that an interplay of a periodic forcing and colored noise can cause a variety of nonequilibrium cooperation effects such as sign reversals of the interspike interval correlations versus noise switching rate as well as versus the frequency of periodic forcing a power law like decay of oscillations of the serial correlation coefficients in the long lag limit amplification of the output signal modulation in the instantaneous firing rate of the neural response etc the features of spike statistics in the limits of slow and fast noises are also discussed

what should a statistical mechanics satisfy to reflect nature there is no compelling reason imposing that the methods of statistical mechanics should be restricted to the dynamical systems which follow the usual boltzmann gibbs prescriptions more specifically ubiquitous natural and artificial systems exhibit generic stationary states which are not ergodic nor close to it in any geometrically simple subset of the a priori allowed phase space in any even extended trivial sense a vast class of such systems appears nevertheless to be tractable within thermostatistical methods completely analogous to the usual ones the question posed in the title arises then naturally some answer to this complex question is advanced in the present review of nonextensive statistical mechanics and its recent connections

computing a non maxwellian velocity distribution from first principles we investigate a family of single particle anomalous velocity distribution by solving a particular class of stochastic liouville equations the stationary state is obtained analytically and the maxwell boltzmann distribution is reobtained in a particular limit we discuss the comparison with other different methods to obtain the stationary state extensions when the models cannot be solved in an exact way are also pointed out in connection with the one ficton approximation

a note on graded yang baxter solutions as braid monoid invariants we construct two osp n mod 2m solutions of the graded yang baxter equation by using the algebraic braid monoid approach the factorizable s matrix interpretation of these solutions is also discussed

functional characterization of generalized langevin equations we present an exact functional formalism to deal with linear langevin equations with arbitrary memory kernels and driven by an arbitrary noise structure characterized through its characteristic functional no other hypothesis is assumed over the noise neither do we use the fluctuation dissipation theorem we find that the characteristic functional of the linear process can be expressed in terms of noise functional and the green function of the deterministic memory like dissipative dynamics this yields a procedure for calculating the full kolmogorov hierarchy of the non markov process as examples we have characterized through the 1 time probability a noise induced interplay between the dissipative dynamics and the structure of different noises conditions that lead to non gaussian statistics and distributions with long tails are analysed the introduction of arbitrary fluctuations in fractional langevin equations has also been pointed out

ordered cumulant technique and differential equations for probability density abstract this paper is concerned with stochastic differential equations of langevin type in which the stochastic forces are gaussian and not of white noise type the problem of finding explicitly the differential equation for the probability density of the process is solved by means of an expansion in the small correlation time of the noise for this purpose we will use the cumulant technique different situations are studied such as markovian or fokker planck equation first correction to the markovian approximation but with the fokker planck form and the corrections of non fokker planck form

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

constructing a statistical mechanics for beck cohen superstatistics the basic aspects of both boltzmann gibbs bg and nonextensive statistical mechanics can be seen through three different stages first the proposal of an entropic functional s bg k sigma i p i ln p i for the bg formalism with the appropriate constraints sigma i p i 1 and sigma i p i e i u for the bg canonical ensemble second through optimization the equilibrium or stationary state distribution p i e betae i z bg with z bg sigma j e betae j for bg third the connection to thermodynamics e g f bg 1 beta ln z bg and u bg partial differential partial differential beta ln z bg assuming temperature fluctuations beck and cohen recently proposed a generalized boltzmann factor b e integral infinity 0 dbetaf beta e betae this corresponds to the second stage described above in this paper we solve the corresponding first stage i e we present an entropic functional and its associated constraints which lead precisely to b e we illustrate with all six admissible examples given by beck and cohen

on the diffusion induced by alternating renewal processes abstract a class of stochastic differential equations driven by non markovian dichotomous processes is studied analytically the exact transition probability density is calculated in opposition to the pure diffusive situations the transport mechanism obtained here has finite velocity some illustrations are worked out explicitly

consistency stability intervals for a judgement in ahp decision support systems abstract this paper focuses on the need to evaluate the consistency of human judgements in decision support systems dss in this sense and in the context of one of the most applied multicriteria methodologies the analytic hierarchy process ahp we obtain the consistency stability interval csi associated with each judgement that is to say the interval in which this can oscillate without exceeding a value of the consistency measure fixed in advance to calculate these csis we consider the row geometric mean method as the priorisation procedure the geometric consistency index as the consistency measure and a local situation with one criterion the proposed procedure has been implemented in a module that is easily adaptable to any decision support system based on ahp

an integral algorithm for numerical integration of one dimensional additive colored noise problems we present an integral closed algorithm for solving a langevin equation driven by an additive colored noise both the mean first passage time in a bistable system and the diffusion current in a titled periodic potential are calculated and the comparison with existing algorithms is carried out the dependence of the numerical results on the time steps is studied our algorithm is shown to have high accuracy and stability

ito versus stratonovich a survey is given of the facts and fancies concerning the nonlinear langevin or ito equation actually it is merely a pre equation which becomes an equation when an interpretation rule is added the rules of ito and stratonovich differ but both are mathematically consistent and therefore equally admissible conventions the reason why they seem to lead to physical differences is that the langevin approach used to arrive at the equation involves a tacit assumption for systems with external noise this assumption can be justified and it is then clear that the stratonovich rule applies systems with internal noise however can only be properly described by a master equation and the ito stratonovich controversy never enters afterward one is free to model the resulting fluctuations either with an ito or a stratonovich scheme but that does not lead to any new information

harmonic potential driven by long range correlated noise the probability distribution of a particle in a quadratic potential driven by gaussian long range correlated noise has been obtained the long time asymptotic relaxation of the stochastic process has been characterized in terms of the long range correlated noise appearing in the corresponding stochastic differential equation defining the process the particular case when the particle is driven by a gaussian color noise has also been revisited in this way giving its exact probability distribution for all time by using a characteristic functional technique reported previously results for a non gaussian long range correlated noise are also shown emphasis has been placed on solving the plane rotator in the presence of arbitrary random torques having long range correlations in order to show strong and weak non markovian effects coming from different sources of noise the undamped free particle under the influence of arbitrary accelerations has been analyzed we also analyze in detail the structure of the trajectories of the overdamped and undamped free particle

nonextensivity of the cyclic lattice lotka volterra model this niteness only oc curs for q 0 5 for the d 2 growth mode growing droplet and for q 0 for the d 1 one growing stripe this strongevidence of nonextensivity is consistent with the spontaneousemergence of local domains of identical particles with fractalboundaries and competing interactions such direct evidenceis for the rst time exhibited for a many body system which at the mean eld level is conservative keywords lattice lotka volterra model fractals reac tion limited processes nonextensivity pacs numbers 5 40 a 05 10 ln 05 65 b 82 40 npmany natural and arti cial systems are known today tobe hardly or not at all tractable within boltzmann gibbsstatistical mechanics hence the usual thermodynamics suchis the case of systems which include long range interactionsor long range microscopic or mesoscopic memory or othersources of multi fractality phenomena where many spa tial and or temporal scales are involved typically exhibitpower laws the celebrated boltzmann gibbs bg entropys

anomalous fluctuation properties we complement and extend our work on fluctuations arising in nonequilibrium systems in steady states driven by l evy noise h touchette and e g d cohen phys rev e 76 020101 r 2007 as a concrete example we consider a particle subjected to a drag force and a l evy white noise with tail index ensuremath mu 0 2 and calculate the probability distribution of the work done on the particle by the drag force as well as the probability distribution of the work dissipated by the dragged particle in a nonequilibrium steady state for 0l ensuremath mu l2 both distributions satisfy what we call an anomalous fluctuation property characterized by positive and negative fluctuations that asymptotically have the same probability for ensuremath mu 2 by contrast the work and dissipated work distributions satisfy the known conventional and extended fluctuation relations respectively which are both characterized by positive fluctuations that are exponentially more probable than negative fluctuations the difference between these different fluctuation behaviors is discussed in the context of large deviation theory experiments that could probe or reveal an anomalous fluctuation property are also discussed

the generalized ornstein uhlenbeck process langevin like equations have been studied in the presence of arbitrary noise the characteristic functional of the generalized langevin process has been built up exact results for all cumulants are given particular stress has been put on the campbell dichotomous and radioactive decay noises transient relaxation susceptibility and diffusion constants for different noisy media have been sketched in order to exemplify the theory the generalized ornstein uhlenbeck and wiener processes have been completely characterized the generalized kubo oscillator has been worked out and all its 1 time moments have been calculated for different noise structures

effects of transient subordinators on the firing statistics of a neuron model driven by dichotomous noise the behavior of a stochastic perfect integrate and fire pif model of neurons is considered the effect of temporally correlated random activity of synaptic inputs is modeled as a combination of an asymmetric dichotomous noise and a random operation time in the form of an inverse strictly increasing levy type subordinator using a first passage time formulation we find exact expressions for the output interspike interval isi statistics particularly it is shown that at some parameter regimes the isi density exhibits a multimodal structure moreover it is demonstrated that the coefficient of variation the serial correlation coefficient and the fano factor display a nonmonotonic dependence on the mean input current i e the isi s regularity is maximized at an intermediate value of the features of spike statistics analytically revealed in our study are compared with previously obtained results for a perfect integrate and fire neuron model driven by dichotomous noise without subordination

stochastic escape processes from a nonsymmetric potential normal form the lifetime from the normal form x ax2 b square root epsilon xi t is analytically studied in terms of the escape time of leaving the unstable point x 0 a perturbation theory in the small noise parameter square root epsilon is introduced to analyse the escape of the stochastic paths we show that the first passage time density satisfies a scale transformation the anomalous fluctuation of the phase space variable x t when there is saturation in the potential of the normal form is analytically calculated using an instanton like approximation an emphasis is placed on thermal explosions in order to exemplify a system undergoing hysteresis in a first order non equilibrium phase transition we carried out monte carlo simulations showing excellent agreement with our theoretical predictions

exact dynamics of stochastic linear delayed systems application to spatiotemporal coordination of comoving agents delayed dynamics result from finite transmission speeds of a signal in the form of energy mass or information in stochastic systems the resulting lagged dynamics challenge our understanding due to the rich behavioral repertoire encompassing monotonic oscillatory and unstable evolution despite the vast literature quantifying this rich behavior is limited by a lack of explicit analytic studies of high dimensional stochastic delay systems here we fill this gap for systems governed by a linear langevin equation of any number of delays and spatial dimensions with additive gaussian noise by exploiting laplace transforms we are able to derive an exact time dependent analytic solution of the langevin equation by using characteristic functionals we are able to construct the full time dependence of the multivariate probability distribution of the stochastic process as a function of the delayed and nondelayed random variables as an application we consider interactions in animal collective movement that go beyond the traditional assumption of instantaneous alignment we propose models for coordinated maneuvers of comoving agents applicable to recent empirical findings in pigeons and bats whereby individuals copy the heading of their neighbors with some delay we highlight possible strategies that individual pairs may adopt to reduce the variance in their velocity difference and or in their spatial separation we also show that a minimum in the variance of the spatial separation at long times can be achieved with certain ratios of measurement to reaction delay

levy noise levy flights levy fluctuations this paper is concerned with a levy noise characterized for t 0 by the functional with 0 2 then levy flights can be defined through a stochastic differential equations rather than the usual chapmann kolmogorov equation we have used this functional approach to solve a plane rotor in the presence of levy noise the linear damped stochastic process driven by levy noise is revisited and its non autonomous and non markovian generalizations have been solved in the context of our functional analysis

finite correlation time effects in nonequilibrium phase transitions i dynamic equation and steady state properties abstract we determine an approximate renormalized equation of evolution for an arbitrary nonlinear single degree of freedom system externally driven by gaussian parametric fluctuations of finite correlation time the renormalization scheme used here gives a second order equation with a time and state dependent diffusion coefficient we are able to calculate the diffusion coefficient in closed form the steady state distribution can easily be obtained from the evolution equation we are thus able to determine the parameter dependence of the steady state distribution and in particular the influence of a correlation time of the fluctuations which does not vanish on the steady state distribution

stochastic resonance reverse resonance and resonant activation induced by a multi state noise abstract in this paper we investigate the periodic response for a linear system driven by a multiplicative multi state noise which is composed of the multiplication of two dichotomous noises to an input temporal oscillatory signal and the escape of brownian particles over the fluctuating potential barrier for a system with a piece wise linear potential and driven by an additive multi state noise which is also composed of the multiplication of two dichotomous noises for the first system we get the stochastic resonance phenomenon for the amplitude of the periodic response vs the two dichotomous noise strengths and the phenomenon of reverse resonance for the amplitude of the periodic response vs k which represents the asymmetry degree of the dichotomous noises for the second system we obtain the resonant activation phenomenon for which the mean first passage time of the brownian particles over the fluctuating potential barrier shows a minimum as the function of the transition rates of the multi state noise

weight stability intervals in multicriteria decision aid abstract in this paper we study the stability of the results given by a wide class of mcda methods to changes of the weights of the criteria three aspects of stability are discussed in each case we propose to construct stability intervals for the weights of either single criteria or groups of criteria a necessary and sufficient condition for stability is also considered the use of these instruments is demonstrated with a numerical example

langevin like equation with colored noise consider a stochastic differential equation of the form of a langevin equation but in which the noise source is not white if it is nearly white i e its autocorrelation time is short a systematic approximation method is known it leads to a fokker planck equation with successive higher order corrections to obtain the coefficients more explicitly a secondary expansion may be employed the validity of the resulting double series approximation is discussed and confronted with the various results given in the literature in addition an alternative approximation method is obtained using the technique for eliminating fast variables it produces the same terms in a different sequence

yang baxterization of braid group representations for a given braid group representation bgr a process of the yang baxterization is formulated to generate solutions of the yang baxter equation ybe when a bgr admits the birman wenzl bw algebraic structure this process can be explicitly passed through and two types of trigonometric solutions of ybe are generated from such a bgr these two solutions have the essential difference to each other and both of them preserve the crossing symmetry property if the given bgr has by taking certain reduction on the bw algebra the rational solution is also generated a practical condition to judge whether a bgr satisfies the bw algebra is given from which one finds that not only the familiar bgrs of 5 7 9 but also some new ones obtained recently in 12 have the bw structure thus they can be explicitly yang baxterized to solutions of the ybe

functional characterization of linear delay langevin equations we present an exact functional characterization of linear delay langevin equations driven by any noise structure defined through its characteristic functional this method relies on the possibility of finding an explicitly analytical expression for each realization of the delayed stochastic process in terms of those of the driving noise general properties of the transient dissipative dynamics are analyzed the corresponding interplay with a color gaussian noise is presented as a full application of our functional method we study a model for population growth with non gaussian fluctuations the gompertz model driven by multiplicative white shot noise

numerical method for solving stochastic differential equations with dichotomous noise we propose a numerical method for solving stochastic differential equations with dichotomous markov noise the numerical scheme is formulated such that i the stochastic formula used follows the stratonovichtaylor form over the entire range of noise correlation times including the gaussian white noise limit and ii the method is readily applicable to dynamical systems driven by arbitrary types of noise provided there exists a way to describe the random increment of the stochastic process expressed in the stratonovich taylor form we further propose a simplified taylor scheme that significantly reduces the computation time while still satisfying the moment properties up to the required order the accuracies and efficiencies of the proposed algorithms are validated by applying the schemes to two prototypical model systems that possess analytical solutions

generalized ornstein uhlenbeck process by doob s theorem and the time evolution of financial prices abstract we generalize the ornstein uhlenbeck ou process using doob s theorem we relax the gaussian and stationary conditions assuming a linear and time homogeneous process the proposed generalization retains much of the simplicity of the original stochastic process while exhibiting a somewhat richer behavior analytical results are obtained using transition probability and the characteristic function formalism and compared with empirical stock market data which are notorious for the non gaussian behavior the analysis focus on the decay patterns and the convergence study of the first four cumulants considering the logarithmic returns of stock prices it is shown that the proposed model offers a good improvement over the classical ou model

the availability of logical operation induced by dichotomous noise for a nonlinear bistable system instead of a continuous system driven by gaussian white noise logical stochastic resonance will be investigated in a nonlinear bistable system with two thresholds driven by dichotomous noise which shows a phenomenon different from gaussian white noise we can realize two parallel logical operations by simply adjusting the values of these two thresholds besides to quantify the reliability of obtaining the correct logic output we numerically calculate the success probability and effects of dichotomous noise on the success probability are observed these observations show that the reliability of realizing logical operation in the bistable system can be improved through optimizing parameters of dichotomous noise

nonextensive statistical mechanics and economics abstract ergodicity this is to say dynamics whose time averages coincide with ensemble averages naturally leads to boltzmann gibbs bg statistical mechanics hence to standard thermodynamics this formalism has been at the basis of an enormous success in describing among others the particular stationary state corresponding to thermal equilibrium there are however vast classes of complex systems which accommodate quite badly or even not at all within the bg formalism such dynamical systems exhibit in one way or another nonergodic aspects in order to be able to theoretically study at least some of these systems a formalism was proposed 14 years ago which is sometimes referred to as nonextensive statistical mechanics we briefly introduce this formalism its foundations and applications furthermore we provide some bridging to important economical phenomena such as option pricing return and volume distributions observed in the financial markets and the fascinating and ubiquitous concept of risk aversion one may summarize the whole approach by saying that bg statistical mechanics is based on the entropy s bg k i p i ln p i and typically provides exponential laws for describing stationary states and basic time dependent phenomena while nonextensive statistical mechanics is instead based on the entropic form s q k 1 i p i q q 1 with s 1 s bg and typically provides for the same type of description asymptotic power laws

stochastic processes driven by dichotomous markov noise some exact dynamical results stochastic processes defined by a general langevin equation of motion where the noise is the non gaussian dichotomous markov noise are studied a non fokker planck master differential equation is deduced for the probability density of these processes two different models are exactly solved in the second one a nonequilibrium bimodal distribution induced by the noise is observed for a critical value of its correlation time critical slowing down does not appear in this point but in another one

on levy or stable distributions and the williams watts model of dielectric relaxation this paper is concerned with the levy or stable distribution function defined by the fourier transform q alpha left z right frac 1 2 pi int infty infty exp left izu left u right alpha right du with 0 alpha leqslant 2 when 2 it becomes the gauss distribution function and when 1 the cauchy distribution when 2 the distribution has a long inverse power tail q alpha left z right sim frac gamma left 1 alpha right sin tfrac 1 2 pi alpha pi left z right 1 alpha in the regime of small if logz 1 the distribution is mimicked by a log normal distribution we have derived rapidly converging algorithms for the numerical calculation ofq z for various in the range 0 1 the functionq z appears naturally in the williams watts model of dielectric relaxation in that model one expresses the normalized dielectric parameter as in n left omega right equiv in n left omega right i in n left omega right int 0 infty e i omega t left d phi left t right mathord left vphantom d phi left t right dt right kern nulldelimiterspace dt right dt with phi left t right exp left t mathord left vphantom t tau right kern nulldelimiterspace tau right alpha it has been found empirically by various authors that observed dielectric parameters of a wide variety of materials of a broad range of frequencies are fitted remarkably accurately by using this form of t e n is shown to be directly related toq z it is also shown that if the williams watts exponential is expressed as a weighted average of exponential relaxation functions exp left t mathord left vphantom t tau right kern nulldelimiterspace tau right alpha int 0 infty g left lambda alpha right e lambda t dt the weight functiong is expressible as a stable distribution some suggestions are made about physical models that might lead to the williams watts form of t

geometry of escort distributions given an original distribution its statistical and probabilistic attributes may be scanned using the associated escort distribution introduced by beck and schlogl and employed in the formulation of nonextensive statistical mechanics here the geometric structure of the one parameter family of the escort distributions is studied based on the kullback leibler divergence and the relevant fisher metric it is shown that the fisher metric is given in terms of the generalized bit variance which measures fluctuations of the crowding index of a multifractal the cramer rao inequality leads to a fundamental limit for the precision of the statistical estimate of the order of the escort distribution we also show quantitatively that it is inappropriate to use the original distribution instead of the escort distribution for calculating the expectation values of physical quantities in nonextensive statistical mechanics

solvability of the master equation for dichotomous flow we consider the one dimensional stochastic flow mathrm x ifmmode dot else fi f x g x ensuremath xi t where ensuremath xi t is a dichotomous markov noise and use a simple procedure to identify the conditions under which the integro differential equation satisfied by the total probability density p x t of the driven variable can be reduced to a differential equation of finite order this generalizes the enumeration of the solvable cases

convergence to the critical attractor of dissipative maps log periodic oscillations fractality and nonextensivity for a family of logisticlike maps we investigate the rate of convergence to the critical attractor when an ensemble of initial conditions is uniformly spread over the entire phase space we found that the phase space volume occupied by the ensemble w t depicts a power law decay with log periodic oscillations reflecting the multifractal character of the critical attractor we explore the parametric dependence of the power law exponent and the amplitude of the log periodic oscillations with the attractor s fractal dimension governed by the inflection of the map near its extremal point further we investigate the temporal evolution of w t for the circle map whose critical attractor is dense in this case we found w t to exhibit a rich pattern with a slow logarithmic decay of the lower bounds these results are discussed in the context of nonextensive tsallis entropies

stochastic algorithms for discontinuous multiplicative white noise stochastic differential equations with multiplicative noise need a mathematical prescription due to different interpretations of the stochastic integral this fact implies specific algorithms to perform numerical integrations or simulations of the stochastic trajectories moreover if the multiplicative noise function is not continuous then the standard algorithms cannot be used we present an explicit algorithm to avoid this problem and we apply it to a well controlled example finally we discuss on the existence of higher order algorithms for this specific situation

statistics of a leaky integrate and fire model of neurons driven by dichotomous noise the behavior of a stochastic leaky integrate and fire model of neurons is considered the effect of temporally correlated random neuronal input is modeled as a colored two level dichotomous markovian noise relying on the riemann method exact expressions for the output interspike interval density and for the serial correlation coefficient are derived and their dependence on noise parameters such as correlation time and amplitude is analyzed particularly noise induced sign reversal and a resonancelike amplification of the kurtosis of the interspike interval distribution are established the features of spike statistics analytically revealed in our study are compared with recently obtained results for a perfect integrate and fire neuron model

method to calculate the moments of the membrane voltage in a model neuron driven by multiplicative filtered shot noise neurons are subject to synaptic inputs from many other cells these inputs consist of spikes changing the conductivity of the target cell i e they enter the neural dynamics as multiplicative shot noise up to now only for simplified models like current based additive noise point neurons or models with gaussian white noise input exact solutions are available we present a method to calculate the exact time dependent moments for the voltage of a point neuron with conductance based shot noise and a passive membrane the exact solutions show features for instance maxima of the moments vs time which are also confirmed by numerical simulations the theoretical analysis of subthreshold membrane fluctuations may contribute to a better comprehension of neural noise in general we also discuss how the analytical results may provide additional conditions for estimating parameters from experimental data

ornstein uhlenbeck cauchy process we combine earlier investigations of linear systems subject to levy fluctuations with recent attempts to give meaning to so called levy flights in external force fields we give a complete construction of the ornstein uhlenbeck cauchy process as a fully computable paradigm example of doob s stable noise supported ornstein uhlenbeck process despite the nonexistence of all moments we determine local characteristics forward drift of the process generators of forward and backward dynamics and relevant pseudodifferential evolution equations the induced nonstationary spatial process is proved to be markovian and quite apart from its inherent discontinuity defines an associated velocity process in a probabilistic sense

a general scheme for studying the stochastic dynamics of a parametric oscillator driven by coloured noise the stochastic dynamics of a classical parametric oscillator driven by coloured noise with exponential correlation is studied both by analytical and numerical methods the critical strength of the parametric modulation at which the motion of the oscillator becomes unbounded and the dependence of this critical strength on the magnitude and the correlation length of the noise are investigated the results show that the critical strength does not depend on either the strength or the correlation length of the coloured noise but that the squeezing induced by the parametric oscillation is enhanced by increasing the correlation length of the noise

delay and memory like langevin equations abstract by using an exact functional formalism we characterize general stationary properties of linear memory like langevin equations including the case of delay equations driven by arbitrary noises spectral properties and stationary distributions are analyzed in detail

dilute birman wenzl murakami algebra and dn 1 2 models a dilute generalization of the birman wenzl murakami algebra is considered it can be baxterized to a solution of the yang baxter algebra the dn 1 2 vertex models constitute a series of solvable lattice models which realize this algebraic structure they can be regarded as a dilute version of the bn 1 vertex models

weak noise expansions through functional integrals for colored noise we use path integral methods to obtain expansions for the correlation functions of the non markovian stochastic processes generated by stochastic differential equations with colored noise

sensitivity analysis for product design selection with an implicit value function abstract in product design selection the decision maker dm often does not have enough information about the end users needs to state the preferences with precision as is required by many of the existing selection methods we present for the case where the dm gives estimates of the preferences a concept for calculating a robustness index the concept can be used with any iterative selection method that chooses a trial design for each iteration and uses the dm s preference parameters at that trial design to eliminate some design options which have lower value than the trial design such methods like our previously published method are applicable to cases where the dm s value function is implicit our robustness index is a metric of the allowed variation between the actual and estimated preferences for which the set of non eliminated trial designs which could be singleton will not change the dm through experience can use the robustness index and other information generated in calculating the index to determine what action to take make a final selection from the present set of non eliminated designs improve the precision of the preference estimates or otherwise cope with the imprecision we present an algorithm for finding the robustness index and demonstrate and verify the algorithm with an engineering example and a numerical example

multi colour braid monoid algebras we define multi colour generalizations of braid monoid algebras and present explicit matrix representations which are related to two dimensional exactly solvable lattice models of statistical mechanics in particular we show that the two colour braid monoid algebra describes the yang baxter algebra of the critical dilute a d e models which were recently introduced by warnaar nienhuis and seaton 1992 as well as by roche 1992 these and other solvable models related to dense and dilute loop models are discussed in detail and it is shown that the solvability is a direct consequence of the algebraic structure it is conjectured that the baxterization of general multi colour braid monoid algebras will lead to the construction of further solvable lattice models

effect of correlated dichotomous noises on stochastic resonance in a linear system a linear system driven by correlated asymmetric dichotomous noises and periodic signal was investigated in the overdamped case the exact expressions of output signal amplitude and signal to noise ratio snr of the system were derived by means of numerical calculations we found that i at some fixed multiplicative noise intensities the output signal amplitude with frequency exhibits the structure of a weak peak even no peak as the dichotomous noise is asymmetric ii in the case of asymmetric dichotomous noise the signal frequency can cause non monotonous behavior of the output signal amplitude with respect to multiplicative noise intensity iii the curve of snr with frequency has a weak peak and a trough in the case of symmetric dichotomous noise but no peak with asymmetric iv whether the multiplicative noise is symmetric or asymmetric the noise can enhance response of the system v the snr increases with the correlation strength between the two noises decreasing in addition the plane of multiplicative noise intensity versus noise symmetric parameter was plotted

equivalent isotropic osp 2 2 spin chains and its bethe ansatz analysis in this paper we discuss the equivalence between two integrable and isotropic osp 2 2 chains via the braid monoid approach we use the analytical bethe ansatz approach in order to solve the spectrum of these systems the ground state is parametrized by a special structure of the bethe ansatz roots their interpretation in terms of correlated fermionic models is briefly discussed