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

stepsize control for mean square numerical methods for stochastic differential equations with small noise a strategy for controlling the stepsize in the numerical integration of stochastic differential equations sdes is presented it is based on estimating the pth mean of local errors the strategy leads to stepsize sequences that are identical for all computed paths for the family of euler schemes for sdes with small noise we derive computable estimates for the dominating term of the pth mean of local errors and show that the strategy becomes efficient for reasonable stepsizes numerical experience is reported for test examples including scalar sdes and a stochastic circuit model

higher order implicit strong numerical schemes for stochastic differential equations higher order implicit numerical methods which are suitable for stiff stochastic differential equations are proposed these are based on a stochastic taylor expansion and converge strongly to the corresponding solution of the stochastic differential equation as the time step size converges to zero the regions of absolute stability of these implicit and related explicit methods are also examined

stabilization of second order evolution equations with unbounded feedback with time dependent delay we consider abstract second order evolution equations with unbounded feedback with time varying delay existence results are obtained under some realistic assumptions we prove the exponential decay under some conditions by introducing an abstract lyapunov functional our abstract framework is applied to the wave to the beam and to the plate equations with boundary delays

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

numerical simulations of stochastic differential equations a simple very accurate algorithm for numerical simulation of stochastic differential equations is described its relationship to colored noise is elucidated and exhibited by explicit results the especially delicate problem of mean first passage times is highlighted and highly accurate agreement between the numerical simulations and analytic results are shown

on the construction of a special class of time inhomogeneous diffusion processes a special class of time inhomogeneous diffusion processes generated starting from gauss markov processes conditioned on the same initial state is considered this class includes many interesting diffusion processes with time dependent infinitesimal drift and variance for which the transition probability density function is explicitly determined moreover closed form results for the first passage time density through suitable time varying boundaries are obtained special cases generated starting from wiener and ornstein uhlenbeck processes are considered and widely discussed

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 transition to sharp timing in stochastic leaky integrate and fire neurons driven by frozen noisy input the firing activity of intracellularly stimulated neurons in cortical slices has been demonstrated to be profoundly affected by the temporal structure of the injected current mainen sejnowski 1995 this suggests that the timing features of the neural response may be controlled as much by its own biophysical characteristics as by how a neuron is wired within a circuit modeling studies have shown that the interplay between internal noise and the fluctuations of the driving input controls the reliability and the precision of neuronal spiking cecchi et al 2000 tiesinga 2002 fellous rudolph destexhe sejnowski 2003 in order to investigate this interplay we focus on the stochastic leaky integrate and fire neuron and identify the holder exponent h of the integrated input as the key mathematical property dictating the regime of firing of a single unit neuron we have recently provided numerical evidence taillefumier magnasco 2013 for the existence of a phase transition when becomes less than the statistical holder exponent associated with internal gaussian white noise h 1 2 here we describe the theoretical and numerical framework devised for the study of a neuron that is periodically driven by frozen noisy inputs with exponent h 0 in doing so we account for the existence of a transition between two regimes of firing when h 1 2 and we show that spiking times have a continuous density when the holder exponent satisfies h 1 2 the transition at h 1 2 formally separates rate codes for which the neural firing probability varies smoothly from temporal codes for which the neuron fires at sharply defined times regardless of the intensity of internal noise

on decay and blow up of the solution for a viscoelastic wave equation with boundary damping and source terms abstract in this paper we consider the decay and blow up properties of a viscoelastic wave equation with boundary damping and source terms we first extend the decay result for the case of linear damping obtained by lu et al on a viscoelastic equation with nonlinear boundary damping and source terms global existence and decay of the solution nonlinear analysis real world applications 12 1 2011 295 303 to the nonlinear damping case under weaker assumption on the relaxation function g t then we give an exponential decay result without the relation between g t and g t for the linear damping case provided that g l 1 0 is small enough finally we establish two blow up results one is for certain solutions with nonpositive initial energy as well as positive initial energy for both the linear and nonlinear damping cases the other is for certain solutions with arbitrarily positive initial energy for the linear damping case

stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks in this paper we consider in a bounded and smooth domain the wave equation with a delay term in the boundary condition we also consider the wave equation with a delayed velocity term and mixed dirichlet neumann boundary condition in both cases under suitable assumptions we prove exponential stability of the solution these results are obtained by introducing suitable energies and by using some observability inequalities if one of the above assumptions is not satisfied some instability results are also given by constructing some sequences of delays for which the energy of some solutions does not tend to zero

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

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

a fourth order algorithm for solving the multi dimensional kramers equation in langevin form we propose a new fourth order numerical method for solving the multi dimensional kramers equation in standard and overdamped regimes the algorithm is developed for modelling the trajectories of airborne particles propagating through porous media such as three dimensional fibre networks it disentangles the deterministic and stochastic parts of the solution so that standard fourth order numerical methods can be used to calculate the deterministic component the stochastic correction to the solution is obtained using a perturbative expansion of the stochastic force in the overdamped regime our method avoids the need for extremely small time steps required by conventional methods we compare the convergence rate of our algorithm to that of other methods by solving the one dimensional duffing equation the proposed algorithm is finally used to evaluate the performance of various filters made from fibres of two different sizes

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

the derivation of the regularized chiral jacobian using the zeta function method using the zeta function method a general formula for the regularized chiral jacobian to theories including non hermitian dirac operators d defined in arbitrary even dimensional euclidean space is derived the agreement of this formula with the results obtained in the differential geometric approach is also clarified

variable step size control in the numerical solution of stochastic differential equations we introduce a variable step size method for the numerical approximation of pathwise solutions to stochastic differential equations sdes the method which is dependent on a representation of bro

a phase transition in the first passage of a brownian process through a fluctuating boundary with implications for neural coding finding the first time a fluctuating quantity reaches a given boundary is a deceptively simple looking problem of vast practical importance in physics biology chemistry neuroscience economics and industrial engineering problems in which the bound to be traversed is itself a fluctuating function of time include widely studied problems in neural coding such as neuronal integrators with irregular inputs and internal noise we show that the probability p t that a gauss markov process will first exceed the boundary at time t suffers a phase transition as a function of the roughness of the boundary as measured by its holder exponent h the critical value occurs when the roughness of the boundary equals the roughness of the process so for diffusive processes the critical value is hc 1 2 for smoother boundaries h 1 2 the probability density is a continuous function of time for rougher boundaries h 1 2 the probability is concentrated on a cantor like set of zero measure the probability density becomes divergent almost everywhere either zero or infinity the critical point hc 1 2 corresponds to a widely studied case in the theory of neural coding in which the external input integrated by a model neuron is a white noise process as in the case of uncorrelated but precisely balanced excitatory and inhibitory inputs we argue that this transition corresponds to a sharp boundary between rate codes in which the neural firing probability varies smoothly and temporal codes in which the neuron fires at sharply defined times regardless of the intensity of internal noise

frictional versus viscoelastic damping in a semilinear wave equation in this article we show exponential and polynomial decay rates for the partially viscoelastic nonlinear wave equation subject to a nonlinear and localized frictional damping the equation that models this problem is given by begin eqnarray u tt kappa 0 delta u int 0 t mbox div a x g t s nabla u s ds f u b x h u t 0 mbox in omega times bbb r quad end eqnarray where a b are nonnegative functions a in c 1 overline omega b in l infty omega satisfying the assumption begin eqnarray a x b x geq delta 0 quad forall x in omega end eqnarray and f and h are power like functions we observe that the assumption 0 2 gives us a wide assortment of possibilities from which to choose the functions a x and b x and the most interesting case occurs when one has simultaneous and complementary damping mechanisms taking this point of view into account a distinctive feature of our paper is exactly to consider different and localized damping mechanisms acting in the domain but not necessarily strategically localized dissipations as considered in the prior literature

a first passage problem for a bivariate diffusion process numerical solution with an application to neuroscience when the process is gauss markov we consider a bivariate gauss markov process and we study the first passage time of one component through a constant boundary we prove that its probability density function is the unique solution of a new integral equation and we propose a numerical algorithm for its solution convergence properties of this algorithm are discussed and the method is applied to the study of the integrated brownian motion and to the integrated ornstein uhlenbeck process finally a model of neuroscience interest is discussed

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

on the regularized determinant for non invertible elliptic operators we propose a technique for regularizing the determinant of a non invertible elliptic operator restricted to the complement of its nilpotent elements we apply this approach to the study of chiral changes in the fermionic path integral variables

global and exponential attractors for extensible thermoelastic plate with time varying delay abstract a class of nonlinear problems modeling thermoelastic extensible plates with rotational inertia and time dependent delay in the internal feedback are considered by virtue of galerkin method combined with the priori estimates we prove the existence and uniqueness of global solution the proof with or without rotational inertia does not depend on the parameters 1 and 2 of time dependent delay moreover the existence of compact global and exponential attractors is proved through a stabilizability estimate this estimate which is established under restrictions on 1 and 2 and independently of the rotational inertia parameter provides bounds on the attractors fractal dimension other property such as additional smoothness of global attractors with respect to parameter is also presented furthermore the existence of a generalized fractal exponential attractor is also derived finally we show that the family of global attractors is continuous with respect to the parameter in some sense

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

not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks we present two examples of hyperbolic partial differential equations which are stabilized by boundary feedback controls and then destabilized by small delays in these controls we show that in a general case when the controls are distributed stabilized hyperbolic systems possess nontrivial periodic solutions if small time delays are introduced into their feedbacks we also indicate by means of an example that the general case of this phenomenon is harder to demonstrate for boundary control problems

fourth order algorithms for solving the multivariable langevin equation and the kramers equation we develop a fourth order simulation algorithm for solving the stochastic langevin equation the method consists of identifying solvable operators in the fokker planck equation factorizing the evolution operator for small time steps to fourth order and implementing the factorization process numerically a key contribution of this paper is to show how certain double commutators in the factorization process can be simulated in practice the method is general applicable to the multivariable case and systematic with known procedures for doing fourth order factorizations the fourth order convergence of the resulting algorithm allowed very large time steps to be used in simulating the brownian dynamics of 121 yukawa particles in two dimensions the converged result of a first order algorithm can be obtained by using time steps 50 times as large to further demonstrate the versatility of our method we derive two new classes of fourth order algorithms for solving the simpler kramers equation without requiring the derivative of the force the convergence of many fourth order algorithms for solving this equation are compared

stochastic calculus in physics the relationship of the ito stratonovich stochastic calculus to studies of weakly colored noise is explained a functional calculus approach is used to obtain an effective fokker planck equation for the weakly colored noise regime in a smooth limit this representation produces the stratonovich version of the ito stratonovich calculus for white noise it also provides an approach to steady state behavior for strongly colored noise numerical simulation algorithms are explored and a novel suggestion is made for efficient and accurate simulation of white noise equations

inverse observability estimates for second order hyperbolic equations with variable coefficients abstract we consider a general second order hyperbolic equation defined on an open bounded domain r n with variable coefficients in both the elliptic principal part and in the first order terms as well at first no boundary conditions b c are imposed our main result theorem 3 5 is a reconstruction or inverse estimate for solutions w under checkable conditions on the coefficients of the principal part the h1 l2 energy at time t t or at time t 0 is dominated by the l2 norms of the boundary traces w a and wt modulo an interior lower order term once homogeneous b c are imposed our results yield under a uniqueness theorem needed to absorb the lower order term continuous observability estimates for both the dirichlet and neumann case with an explicit sharp observability time hence by duality exact controllability results moreover no artificial geometrical conditions are imposed on the controlled part of the boundary in the neumann case in contrast with existing literature the first step of our method employs a riemann geometry approach to reduce the original variable coefficient principal part problem in r n to a problem on an appropriate riemann manifold determined by the coefficients of the principal part where the principal part is the laplacian in our second step we employ explicit carleman estimates at the differential level to take care of the variable first order energy level terms in our third step we employ micro local analysis yielding a sharp trace estimate to remove artificial geometrical conditions on the controlled part of the boundary in the neumann case

on perturbation theory for regularized determinants of differential operators a perturbation theory for determinants of differential operators regularized through the function technique is presented the application of this approach to the study of chiral changes in the fermionic path integral variables is discussed

numerical integration of multiplicative noise stochastic differential equations a two stage runge kutta algorithm for vector ito and by transform also stratonovich stochastic differential equations with multiplicative noise has been developed the method is second order accurate but for vanishing drift the algorithm yields a martingale independent of step size several examples are included to illustrate our method a discussion of errors shows that sample size can be as important as truncation

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

exact propagator for generalized ornstein uhlenbeck processes a closed form expression for the propagator is derived in terms of modified bessel functions for the fokker planck equation for a physically important generalization of the ornstein uhlenbeck process where the diffusion constant d p is a function of the momentum the closed form is found for the general case d p approximately p alpha where alpha or 0 and leads to the standard gaussian form for alpha 0 the propagator for the specific case d p approximately p 1 is used to derive analytic expressions for probability distributions and correlation coefficients an exact expression is found for the constant of proportionality for the anomalous diffusion of the mean square displacement of a particle at short times

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

a haar like construction for the ornstein uhlenbeck process the classical haar construction of brownian motion uses a binary tree of triangular wedge shaped functions this basis has compactness properties which make it especially suited for certain classes of numerical algorithms we present a similar basis for the ornstein uhlenbeck process in which the basis elements approach asymptotically the haar functions as the index increases and preserve the following properties of the haar basis all basis elements have compact support on an open interval with dyadic rational endpoints these intervals are nested and become smaller for larger indices of the basis element and for any dyadic rational only a finite number of basis elements is nonzero at that number thus the expansion in our basis when evaluated at a dyadic rational terminates in a finite number of steps we prove the covariance formulae for our expansion and discuss its statistical interpretation

existence and decay of solutions of a viscoelastic equation with a nonlinear source abstract in a bounded domain we consider u tt u 0 t g t u d u u where 0 and g is a nonnegative and decaying function we prove a local existence theorem and show for certain initial data and suitable conditions on g and that this solution is global with energy which decays exponentially or polynomially depending on the rate of the decay of the relaxation function g

exact numerical simulation of the ornstein uhlenbeck process and its integral a numerical simulation algorithm that is exact for any time step ensuremath delta tg0 is derived for the ornstein uhlenbeck process x t and its time integral y t the algorithm allows one to make efficient unapproximated simulations of for instance the velocity and position components of a particle undergoing brownian motion and the electric current and transported charge in a simple r l circuit provided appropriate values are assigned to the ornstein uhlenbeck relaxation time ensuremath tau and diffusion constant c a simple taylor expansion in ensuremath delta t of the exact simulation formulas shows how the first order simulation formulas which are implicit in the langevin equation for x t and the defining equation for y t are modified in second order the exact simulation algorithm is used here to illustrate the zero ensuremath tau limit theorem textcopyright 1996 the american physical society

accurate monte carlo tests of the stochastic ginzburg landau model with multiplicative colored noise an accurate and fast monte carlo algorithm is proposed for solving the ginzburg landau equation with multiplicative colored noise the stable cases of solution for choosing time steps and trajectory numbers are discussed

method of lyapunov functionals construction in stability of delay evolution equations the investigation of stability for hereditary systems is often related to the construction of lyapunov functionals the general method of lyapunov functionals construction which was proposed by v kolmanovskii and l shaikhet and successfully used already for functional differential equations for difference equations with discrete time for difference equations with continuous time is used here to investigate the stability of delay evolution equations in particular partial differential equations

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 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

uniqueness and stability of an inverse kernel problem for type iii thermoelasticity in this paper we establish a global carleman estimate for a thermoelastic system of type iii based on this estimate we furthermore study an inverse problem of determining a spatially varying thermal kernel function we derive holder stability for the coefficient inverse problem only by displacement measurements over a given subdomain along a sufficiently large time interval and temperature measurements at time t0 over whole domain the uniqueness for such an inverse problem is yielded as a direct result

on the quotient of the regularized determinant of two elliptic operators we study the quotient of the regularized determinants of two elliptic operators having the same principal symbol we prove that under general conditions a method recently proposed by tamura coincides with the function approach

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

general decay of the solution energy in a viscoelastic equation with a nonlinear source abstract in a bounded domain we consider u t t u 0 t g t u d u u where 0 and g is a nonnegative and decaying function we prove that for certain class of relaxation functions and certain initial data the rate of decay of energy is similar to that of g this result improves earlier ones in the literature in which only the exponential and polynomial decay rates are considered

second order algorithm for simulating stochastic differential equations with white noises abstract the second order algorithm for simulating stochastic differential equations with gaussian white noises is presented these stochastic differential equations are universal type among these gaussian white noises come from different sources specifically the proposed algorithm extends previous first order algorithm for stochastic differential equations with different white noises and second order algorithm for stochastic differential equations with same white noise in practice it is proved that this algorithm is scientific

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

general decay rate estimate for a viscoelastic equation with weakly nonlinear time dependent dissipation and source terms a viscoelastic wave equation in canonical form with weakly nonlinear time dependent dissipation and source terms is investigated in this paper for a wider class of relaxation functions and without imposing any restrictive growth assumption on the damping term at the origin we establish an explicit and general energy decay rate result

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

estimation of the input parameters in the ornstein uhlenbeck neuronal model the stochastic ornstein uhlenbeck neuronal model is studied and estimators of the model input parameters depending on the firing regime of the process are derived closed expressions for the laplace transforms of the first two moments of the normalized first passage time through a constant boundary in the suprathreshold regime are derived which is used to define moment estimators in the subthreshold regime the exponentiality of the first passage time is utilized to characterize the input parameters in the threshold regime and for the wiener process approximation analytic expressions for the first passage time density are used to derive the maximum likelihood estimators of the parameters the methods are illustrated on simulated data under different conditions including misspecification of the intrinsic parameters of the model finally known approximations of the first passage time moments are improved

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

computer simulations of multiplicative stochastic differential equations a class of robust algorithms for the computer simulation of stochastic differential equations with multiplicative noise is investigated excellent agreement is obtained with the known analytic behaviour of the kubo oscillator in the white noise limit the algorithms include a known first order one dimensional explicit method as well as implicit methods of increased stability a distinction is drawn between classes of stochastic differential equations depending on the type of spatial variation or curvature defined by the diffusion tensor this allows greatly simplified numerical implementations of the new algorithms in certain cases the results of different techniques are compared for the case of the kubo oscillator where a semi implicit technique gives the greatest accuracy

convergence to diffusion waves of solutions to nonlinear viscoelastic model with fading memory we study the large time behavior inl2 of solutions to a model for the motion of an unbounded homogeneous viscoelastic bar with fading memory decay rates for the solutions are obtained under the assumption that the initial data and histories are smooth and small moreover convergence of the solutions to diffusion waves which are solutions of burgers equations is proved and rates are obtained our method is based on the study of properties of the solutions to the linearized system in the fourier space

functional determinants for ordinary differential operators the authors study the analytic properties of regularized functional determinants for ordinary differential operators to this end a new regularization scheme is introduced relations between different approaches are analysed and the connection between the presence of divergent traces and regularization differences is discussed

computation of lyapunov spectra effect of interactive noise and application to a chemical oscillator abstract a refined version of the sano sawada algorithm to compute lyapunov spectra has been implemented and tested with several models which include periodic chaotic and hyperchaotic attractors under conditions designed to mimic experimental situations it was found that reliable lyapunov exponents can be obtained for time series of moderate length and point density also in the presence of interactive noise as long as its amplitude does not exceed 1 of the oscillation amplitude the algorithm was then applied to experimental data from the co oxidation on pt 110 clearly showing the occurrence of chaos as well as hyperchaos

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

integrated stationary ornstein uhlenbeck process and double integral processes abstract we find a representation of the integral of the stationary ornstein uhlenbeck isou process in terms of brownian motion b t moreover we show that under certain conditions on the functions f and g the double integral process dip d t t g s s f u d b u d s can be thought as the integral of a suitable gauss markov process some theoretical and application details are given among them we provide a simulation formula based on that representation by which sample paths probability densities and first passage times of the isou process are obtained the first passage times of the dip are also studied

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

analysis of reflected diffusions via an exponential time based transformation let x t be a time homogeneous diffusion process with state space 0 infty where 0 is a reflecting or entrance endpoint and let z denote a random variable that describes the process x t evaluated at an exponentially distributed random time we propose a method to obtain closed form expressions for the conditional density and the mean of a new diffusion process y t with the same state space and with the same infinitesimal variance whose drift depends on the infinitesimal moments of x t and on the hazard rate function of z this method also allows us to obtain the laplace transform of the first passage time density of y t through a lower constant boundary we then discuss the relation between y t and the process x t subject to catastrophes as well as the interpretation of y t as a diffusion in a decreasing potential we study in detail some special cases concerning diffusion processes obtained when x t is the wiener ornstein uhlenbeck bessel and rayleigh process

estimating nonstationary input signals from a single neuronal spike train neurons temporally integrate input signals translating them into timed output spikes because neurons nonperiodically emit spikes examining spike timing can reveal information about input signals which are determined by activities in the populations of excitatory and inhibitory presynaptic neurons although a number of mathematical methods have been developed to estimate such input parameters as the mean and fluctuation of the input current these techniques are based on the unrealistic assumption that presynaptic activity is constant over time here we propose tracking temporal variations in input parameters with a two step analysis method first nonstationary firing characteristics comprising the firing rate and non poisson irregularity are estimated from a spike train using a computationally feasible state space algorithm then information about the firing characteristics is converted into likely input parameters over time using a transformation formula which was constructed by inverting the neuronal forward transformation of the input current to output spikes by analyzing spike trains recorded in vivo we found that neuronal input parameters are similar in the primary visual cortex v1 and middle temporal area whereas parameters in the lateral geniculate nucleus of the thalamus were markedly different

numerical simulations of generalized langevin equations with deeply asymptotic parameters a unified algorithm for solving langevin equations with deeply asymptotic parameters is proposed and tested the method consists of identifying solvable linear friction and implementing the force evaluations by use of the runge kutta method we apply the present scheme to the periodic motion of an overdamped particle subjected to a multiplicative white noise the accurate calculations for the temporal velocity of the particle and its correlation function can be realized by introducing an inertial term it is shown that the fluctuation around the steady quantity increases with decreasing time step in the overdamped white noise algorithm however a massive white noise technique greatly reduces this spurious drift and the result can converge to the correct value if the added inertia approaches zero the other application is the simulation of generalized langevin equation with an exponential memory friction this allows us to treat a weak non markovian process

asymptotic stability of a problem with balakrishnantaylor damping and a time delay in this paper we investigate the asymptotic stability of the viscoelastic kirchhoff equation with balakrishnantaylor damping and a delay term we establish general energy decay result by suitable lyapunov functionals

functional determinants for general sturm liouville problems simple and analytically tractable expressions for functional determinants are known to exist for many cases of interest we extend the range of situations for which these hold to cover systems of self adjoint operators of the sturm liouville type with arbitrary linear boundary conditions the results hold whether or not the operators have negative eigenvalues the physically important case of functional determinants of operators with a zero mode but where that mode has been extracted is studied in detail for the same range of situations as when no zero mode exists the method of proof uses the properties of generalized zeta functions the general form of the final results is the same for the entire range of problems considered

a fast algorithm for the first passage times of gauss markov processes with holder continuous boundaries even for simple diffusion processes treating first passage problems analytically proves intractable for generic barriers and existing numerical methods are inaccurate and computationally costly here we present a novel numerical method that is faster and has more tightly controlled accuracy our algorithm is a probabilistic variant of dichotomic search for the computation of first passage times through non negative homogeneously holder continuous boundaries by gauss markov processes these include the ornstein uhlenbeck process underlying the ubiquitous leaky integrate and fire model of neuronal excitation our method evaluates discrete points in a sample path exactly and refines this representation recursively only in regions where a passage is rigorously estimated to be probable e g when close to the boundary

global and blow up solutions for a system of nonlinear hyperbolic equations with dissipative terms abstract in this paper we study a nonlinear hyperbolic system with strong damping firstly by use of the successive approximation method and a series of classical estimates we prove the local existence and uniqueness of weak solution secondly via some inequalities applying the potential method and the concave method we discuss the asymptotic and blow up behavior of weak solution with different conditions

an example on the effect of time delays in boundary feedback stabilization of wave equations this note is concerned with the erect of time delays in boundary feedback stabilization schemes for wave equations the question to be addressed is whether such delays can destabilize a system which is uniformly asymptotically stable in the absence of delays

general decay of the solution for a viscoelastic wave equation with a time varying delay term in the internal feedback in this paper we consider a viscoelastic wave equation with a time varying delay term the coefficient of which is not necessarily positive by introducing suitable energy and lyapunov functionals under suitable assumptions we establish a general energy decay result from which the exponential and polynomial types of decay are only special cases