variance component testing in generalised linear models with random effects summary there is considerable interest in testing for overdispersion correlation and heterogeneity across groups in biomedical studies in this paper we cast the problem in the framework of generalised linear models with random effects we propose a global score test for the null hypothesis that all the variance components are zero this test is a locally asymptotically most stringent test and is robust in the special sense that the test does not require specifying the joint distribution of the random effects we also propose individual score tests and their approximations for testing the variance components separately both tests can be easily implemented using existing statistical software we illustrate these tests with an application to the study of heterogeneity of mating success across males and females in an experiment on salamander matings and evaluate their performance through simulation

a lyapunov like characterization of asymptotic controllability it is shown that a control system in bf r n is asymptotically controllable to the origin if and only if there exists a positive definite continuous functional of the states whose derivative can be made negative by appropriate choices of controls

a multivariate two sample mean test for small sample size and missing data we develop a new statistic for testing the equality of two multivariate mean vectors a scaled chi squared distribution is proposed as an approximating null distribution because the test statistic is based on componentwise statistics it has the advantage over hotelling s t2 test of being applicable to the case where the dimension of an observation exceeds the number of observations an appealing feature of the new test is its ability to handle missing data by relying on only componentwise sample moments monte carlo studies indicate good power compared to hotelling s t2 and a recently proposed test by srivastava 2004 technical report university of toronto the test is applied to drug discovery data

intensity approximation of random fluctuation in complex systems abstract the markov and non markov processes in complex systems are examined with the help of dynamical information shannon entropy method here we consider the essential role of two mutually independent channels of entropy involving creation of correlation and annihilation of correlation the developed method has been used to analyze the intensity fluctuation of the complex systems of various nature in psychology to analyze numerical and pattern short time human memory to study the effect of stress on the parameters of the dynamical taping test and in cardiology to analyze the random dynamics of rr intervals in human ecg s and to diagnose various diseases of human cardiovascular systems the received results show that the application of intensity approximation allows to improve essentially the diagnostics of parameters in the evolution of human dynamic states

effect of non gaussian noise sources in a noise induced transition here we study a noise induced transition when the system is driven by a noise source taken as colored and non gaussian we show using both a theoretical approximation and numerical simulations that there is a shift of the transition as the noise departs from the gaussian behavior also we confirm the reentrance effect found for colored gaussian noise and show the behavior of the transition line in the phase like diagram as the noise departs from gaussianity in the large correlation time limit

random matrix ensembles from nonextensive entropy the classical gaussian ensembles of random matrices can be constructed by maximizing boltzmann gibbs shannon s entropy s text bgs ensuremath ensuremath int d mathbf h p mathbf h mathrm ln p mathbf h with suitable constraints here we construct and analyze random matrix ensembles arising from the generalized entropy s q 1 ensuremath ensuremath int d mathbf h p mathbf h q q ensuremath 1 thus s 1 s text bgs the resulting ensembles are characterized by a parameter q measuring the degree of nonextensivity of the entropic form making q ensuremath rightarrow 1 recovers the gaussian ensembles if q ensuremath ne 1 the joint probability distributions p mathbf h cannot be factorized i e the matrix elements of mathbf h are correlated in the limit of large matrices two different regimes are observed when ql1 p mathbf h has compact support and the fluctuations tend asymptotically to those of the gaussian ensembles anomalies appear for qg1 both p mathbf h and the marginal distributions p h ij show power law tails numerical analyses reveal that the nearest neighbor spacing distribution is also long tailed not wigner dyson and after proper scaling very close to the result for the 2 ifmmode times else texttimes fi 2 case char22 a generalization of wigner s surmise we discuss connections of these nonextensive ensembles with other non gaussian ones such as the so called l evy ensembles and those arising from soft confinement

semiparametric regression for clustered data we consider estimation in a semiparametric partially generalised linear model for clustered data using estimating equations a marginal model is assumed where the mean of the outcome variable depends on some covariates parametrically and a cluster level covariate nonparametrically a profile kernel method allowing for working correlation matrices is developed we show that the nonparametric part of the model can be estimated using standard nonparametric methods including smoothing parameter estimation and the parametric part of the model can be estimated in a profile fashion the asymptotic distributions of the parameter estimators are derived and the optimal estimators of both the nonparametric and parametric parts are shown to be obtained when the working correlation matrix equals the actual correlation matrix the asymptotic covariance matrix of the parameter estimator is consistently estimated by the sandwich estimator we show that the semiparametric efficient score takes on a simple form and our profile kernel method is semiparametric efficient the results for the case where the nonparametric part of the model is an observation level covariate are noted to be dramatically different

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

a multi interacting agent model for financial markets abstract microscopic models which resemble random magnetic systems have been used recently in the literature for the description of financial markets in the present work a model with many interacting agents similar to an ising random magnet with infinite range interactions is investigated the introduction of a local field term depending on the absolute value of a magnetization like parameter which measures the volatility of a financial market leads to a significant improvement with respect to previously studied models in the literature by investigating the return time series we show that several features characteristic of real financial markets are better reproduced by the present model in particular within this approach one is able to provide a proper behavior for the following properties i the power law tails and the nonzero skewness of the probability distribution of returns ii the exponential decay of the two time autocorrelation function of returns typical of high frequency financial data iii the so called leverage effect which corresponds to a negative correlation between past returns and future volatility

enhancement of stochastic resonance the role of non gaussian noises abstract we have analyzed the phenomenon of stochastic resonance in a double well potential driven by a colored non gaussian noise using a path integral approach we have obtained a consistent markovian approximation that enables us to get through the two state theory analytical expressions for the signal to noise ratio finding an enhancement of this quantity when the system departs from gaussian behavior this finding is supported by extensive numerical simulations we discuss the relation of these results to some experiments in sensory systems

the effects of mixture distribution misspecification when fitting mixed effects logistic models summary mixed effects logistic models are often used to analyze binary response data which have been gathered in clusters or groups responses are assumed to follow a logistic model within clusters with an intercept which varies across clusters according to a specified probability distribution g in this paper we examine the performance of mixed effects logistic regression analysis when a main component of the model the mixture distribution is misspecified we show that when the mixture distribution is misspecified estimates of model parameters including the effects of covariates typically are asymptotically biased i e inconsistent however we present some approximations which suggest that the magnitude of the bias in the estimated covariate effects is typically small these findings are corroborated by a set of simulations which also suggest that valid variance estimates of estimated covariate effects can be obtained when the mixture distribution is misspecified

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

stabilization with discounted optimal control abstract we provide a condition under which infinite horizon discounted optimal control problems can be used in order to obtain stabilizing controls for nonlinear systems the paper gives a mathematical analysis of the problem as well as an illustration by a numerical example

relaxation in heterogeneous systems a rare events dominated phenomenon abstract we have derived a general two power law relaxation function for heterogeneous materials using the maximum entropy principle for nonextensive systems the power law exponents of the relaxation function are simply related to a global fractal parameter and for large time to the entropy nonextensivity parameter q for intermediate times the relaxation follows a stretched exponential behavior the asymptotic power law behaviors both in the time and the frequency domains coincide with those of the weron generalized dielectric function derived in the stochastic theory from an extension of the levy central limit theorem these results are in full agreement with the jonscher universality principle and trace the origin of the large t power law universality with system dependent exponent and q to the scaling behavior of the extreme value distribution function of the effective macroscopic waiting time and the fluctuation of the number of relaxing entities

misspecified maximum likelihood estimates and generalised linear mixed models summary we investigate the impact of model violations on the estimate of a regression coefficient in a generalised linear mixed model specifically we evaluate the asymptotic relative bias that results from incorrect assumptions regarding the random effects we compare the impact of model violation for two parameterisations of the regression model substantial bias in the conditionally specified regression point estimators can result from using a simple random intercepts model when either the random effects distribution depends on measured covariates or there are autoregressive random effects a marginally specified regression structure that is estimated using maximum likelihood is much less susceptible to bias resulting from random effects model misspecification

stabilization of strictly dissipative discrete time systems with discounted optimal control abstract we consider stabilization of an equilibrium point via infinite horizon discounted optimal control in discrete time in addition to applications in economics and social sciences discounted optimal control is a commonly used numerical technique guaranteeing solvability of certain classes of optimal control problems in this paper we present conditions based on strict dissipativity that ensure that the optimally controlled system is asymptotically stable or practically asymptotically stable these conditions are shown to be complementary to recently proposed conditions based on a detectability property illustrative examples are provided

law of error in tsallis statistics in order to theoretically explain the ubiquitous existence of power law behavior such as chaos and fractals in nature tsallis entropy has been successfully applied to the generalization of the traditional boltzmann gibbs statistics the fundamental information measure of which is shannon entropy tsallis entropy s sub q is a one parameter generalization of shannon entropy s sub 1 in the sense that lim sub q spl rarr 1 s sub q s sub 1 the generalized statistics using tsallis entropy are referred to as tsallis statistics in order to present the law of error in tsallis statistics as a generalization of gauss law of error and prove it mathematically we apply the new multiplication operation determined by q logarithm and q exponential the fundamental functions in tsallis statistics to the definition of the likelihood function in gauss law of error the present maximum likelihood principle mlp leads us to determine the so called q gaussian distribution which coincides with one of the tsallis distributions derived from the maximum entropy principle for tsallis entropy under the second moment constraint

analysis and design of unconstrained nonlinear mpc schemes for finite and infinite dimensional systems we present a technique for computing stability and performance bounds for unconstrained nonlinear model predictive control mpc schemes the technique relies on controllability properties of the system under consideration and the computation can be formulated as an optimization problem whose complexity is independent of the state space dimension based on the insight obtained from the numerical solution of this problem we derive design guidelines for nonlinear mpc schemes which guarantee stability of the closed loop for small optimization horizons these guidelines are illustrated by a finite and an infinite dimensional example

on the stability of receding horizon control with a general terminal cost we study the stability and region of attraction properties of a family of receding horizon schemes for nonlinear systems using dini s theorem on the uniform convergence of functions we show that there is always a finite horizon for which the corresponding receding horizon scheme is stabilizing without the use of a terminal cost or terminal constraints after showing that optimal infinite horizon trajectories possess a uniform convergence property we show that exponential stability may also be obtained with a sufficient horizon when an upper bound on the infinite horizon cost is used as terminal cost combining these important cases together with a sandwiching argument we are able to conclude that exponential stability is obtained for input constrained receding horizon schemes with a general nonnegative terminal cost for sufficiently long horizons region of attraction estimates are also included in each of the results

diagnosis of random effect model misspecification in generalized linear mixed models for binary response summary generalized linear mixed models glmms are widely used in the analysis of clustered data however the validity of likelihood based inference in such analyses can be greatly affected by the assumed model for the random effects we propose a diagnostic method for random effect model misspecification in glmms for clustered binary response we provide a theoretical justification of the proposed method and investigate its finite sample performance via simulation the proposed method is applied to data from a longitudinal respiratory infection study

diagnosing misspecification of the random effects distribution in mixed models it is traditionally assumed that the random effects in mixed models follow a multivariate normal distribution making likelihood based inferences more feasible theoretically and computationally however this assumption does not necessarily hold in practice which may lead to biased and unreliable results we introduce a novel diagnostic test based on the so called gradient function proposed by verbeke and molenberghs 2013 to assess the random effects distribution we establish asymptotic properties of our test and show that under a correctly specified model the proposed test statistic converges to a weighted sum of independent chi squared random variables each with one degree of freedom the weights which are eigenvalues of a square matrix can be easily calculated we also develop a parametric bootstrap algorithm for small samples our strategy can be used to check the adequacy of any distribution for random effects in a wide class of mixed models including linear mixed models generalized linear mixed models and non linear mixed models with univariate as well as multivariate random effects both asymptotic and bootstrap proposals are evaluated via simulations and a real data analysis of a randomized multicenter study on toenail dermatophyte onychomycosis

effective markovian approximation for non gaussian noises a path integral approach abstract we have analyzed diffusion in a double well potential driven by a colored non gaussian noise using a path integral approach we have obtained a consistent markovian approximation to the initially non markovian problem such an approximation allows us to get analytical expressions for the mean first passage time that has been tested against extensive numerical simulations

bounded noise induced transitions in a tumor immune system interplay by studying a recent biophysical model of tumor growth in the presence of the immune system here we propose that the phenomenon of evasion of tumors from immune control at a temporal mesoscale might in some cases be due to random fluctuations in the levels of the immune system bounded noises are considered but the gaussian approach is also used for analytical reference after showing that in the case of bounded noises there may be multiple attractors in the space of probability densities we numerically show that the velocity of convergence toward asymptotic density is very slow and that a transitory analysis is needed then by simulations using the sine wiener and the tsallis noises we show that if the level of the noise is sufficiently large then there may be the onset of noise induced transitions in the transitory density evaluated at realistic times namely the transitions are from unimodal density centered at low values of tumor burden to bimodal densities that have a second maximum centered at higher values however those transitions depend on the distribution of the noise

a note on the bias of estimators with missing data it is well known that many standard analyses including maximum likelihood estimation and the generalized estimating equation approach liang and zeger 1986 biometrika 73 13 22 can result in biased estimation when there are missing observations in such cases it is of interest to calculate the magnitude of the bias incurred under specific assumptions about the process generating the full data and the nonresponse mechanism in this paper we give a condition that identifies the limit in probability of estimators that are solutions of estimating equations computed from the incomplete data with discrete data this condition suggests a simple algorithm to compute the asymptotic bias of these estimators that can be easily implemented with existing statistical software we illustrate our approach with asthma prevalence data in children

solution to the hjb equation for lqr type problems on compact connected lie groups in this paper we provide a solution to the hjb equation associated with lqr type problems for fully actuated left invariant control systems on compact connected lie groups we obtain the corresponding algebraic differential riccati equation and in turn generalize some of the results in berkane and tayebi 2015 to a broader class of lie groups closed loop stability results are also derived

on the gaussian q distribution we present a study of the gaussian q measure introduced by diaz and teruel from a probabilistic and from a combinatorial viewpoint a main motivation for the introduction of the gaussian q measure is that its moments are exactly the q analogues of the double factorial numbers we show that the gaussian q measure interpolates between the uniform measure on the interval 1 1 and the gaussian measure on the real line 2009 elsevier inc all rights reserved

a generalization of the cumulant expansion application to a scale invariant probabilistic model as well known cumulant expansion is an alternative way to moment expansion to fully characterize probability distributions provided all the moments exist if this is not the case the so called escort mean values or q moments have been proposed to characterize probability densities with divergent moments c tsallis et al j math phys 50 043303 2009 we introduce here a new mathematical object namely the q cumulants which in analogy to the cumulants provide an alternative characterization to that of the q moments for the probability densities to illustrate the technical details of the procedure we apply this new scheme to further study a recently proposed family of scale invariant discrete probabilistic models a rodriguez et al j stat mech theory exp 2008 p09006 r hanel et al eur phys j b 72 263 2009 having q gaussians as limiting probability distributions

tsallis distributions and 1 f noise from nonlinear stochastic differential equations probability distributions that emerge from the formalism of nonextensive statistical mechanics have been applied to a variety of problems in this article we unite modeling of such distributions with the model of widespread 1 f noise we propose a class of nonlinear stochastic differential equations giving both the q exponential or q gaussian distributions of signal intensity revealing long range correlations and 1 f behavior of the power spectral density the superstatistical framework to get 1 f noise with q exponential and q gaussian distributions of the signal intensity is proposed as well

rates of convergence of non extensive statistical distributions to levy distributions in full and half spaces the levy type distributions are derived using the principle of maximum tsallis non extensive entropy both in the full and half spaces the rates of convergence to the exact levy stable distributions are determined by taking the n fold convolutions of these distributions the marked difference between the problems in the full and half spaces is elucidated analytically it is found that the rates of convergence depend on the ranges of the levy indices an important result emerging from the present analysis is deduced if interpreted in terms of random walks implying the dependence of the asymptotic long time behaviours of the walks on the ranges of the levy indices if n is identified with the total time of the walks

analysis of unconstrained nonlinear mpc schemes with time varying control horizon for discrete time nonlinear systems satisfying an exponential or finite time controllability assumption we present an analytical formula for a suboptimality estimate for model predictive control schemes without stabilizing terminal constraints based on our formula we perform a detailed analysis of the impact of the optimization horizon and the possibly time varying control horizon on stability and performance of the closed loop

type i and type ii error under random effects misspecification in generalized linear mixed models generalized linear mixed models glmms have become a frequently used tool for the analysis of non gaussian longitudinal data estimation is based on maximum likelihood theory which assumes that the underlying probability model is correctly specified recent research is showing that the results obtained from these models are not always robust against departures from the assumptions on which these models are based in the present work we have used simulations with a logistic random intercept model to study the impact of misspecifying the random effects distribution on the type i and ii errors of the tests for the mean structure in glmms we found that the misspecification can either increase or decrease the power of the tests depending on the shape of the underlying random effects distribution and it can considerably inflate the type i error rate additionally we have found a theoretical result which states that whenever a subset of fixed effects parameters not included in the random effects structure equals zero the corresponding maximum likelihood estimator will consistently estimate zero this implies that under certain conditions a significant effect could be considered as a reliable result even if the random effects distribution is misspecified

linear programming approach to deterministic infinite horizon optimal control problems with discounting we investigate relationships between the deterministic infinite time horizon optimal control problem with discounting in which the state trajectories remain in a given compact set y and a certain infinite dimensional linear programming idlp problem we introduce the problem dual with respect to this idlp problem and obtain some duality results we construct necessary and sufficient optimality conditions for the optimal control problem under consideration and we give a characterization of the viability kernel of y we also indicate how one can use finite dimensional approximations of the idlp problem and its dual for construction of near optimal feedback controls the construction is illustrated with a numerical example

statistics of the eigenvalues of tsallis matrices abstract the statistics of the eigenvalues of symmetric random matrices composed by real and statistically independent elements following the distribution that maximizes tsallis s entropy is carried numerically in the limit of large matrices for entropic indexes in the interval 5 3 by using a convenient rescale of variables it is possible to show that such matrices fall in the same class of the gaussian orthogonal ensemble goe for the entropic index 5 3 q the density of eigenvalues and the distribution of level spacings do not seem to follow a simple rescale of variables involving different values of q and exhibit a behavior very distinct from the goe both quantities present long tails for 5 3 q 2 and such long tails die out when q 2 the density of eigenvalues appears to be symmetric around zero exhibiting a peak at the origin that becomes steeper for increasing values of q approaching a delta function at the origin when q 3 the distribution of level spacings displays a form that resembles the well known wigner s surmise augmented by a long tail for q slightly greater than 5 3 but gets deformed for increasing values of q approaching an exponential decay for q 2 for q close to 3 our results resemble those of very sparse random matrices characterized by many zero matrix elements

a smooth nonparametric estimate of a mixing distribution using mixtures of gaussians abstract we propose a method of estimating mixing distributions using maximum likelihood over the class of arbitrary mixtures of gaussians subject to the constraint that the component variances be greater than or equal to some minimum value h this approach can lead to estimates of many shapes with smoothness controlled by parameter h we show that the resulting estimate will always be a finite mixture of gaussians each having variance h the nonparametric maximum likelihood estimate can be viewed as a special case with h 0 the method can be extended to estimate multivariate mixing distributions examples and the results of a simulation study are presented

control lyapunov functions and zubov s method for finite dimensional nonlinear control systems we study the relation between asymptotic null controllability and control lyapunov functions it is shown that control lyapunov functions clfs may be constructed on the domain of asymptotic null controllability as viscosity solutions of a first order pde that generalizes zubov s equation the solution is also given as the value function of an optimal control problem from which several regularity results may be obtained

non extensive block entropy statistics of cantor fractal sets abstract by using non extensive block entropy statistics we demonstrate analytically that the static structures of deterministic cantor sets with fractal dimension d f are characterised by a non extensive q exponent q 1 d f d for d f d where d is the embedding dimensions of the fractal set to calculate the s q entropy we use the block entropy method based on non overlapping windows and standard exact enumeration on cantor sets this result indicates that fractal structures are formed via dynamical processes which operate at the edge of chaos

tsallis threshold analysis of digital speckle patterns generated by rough surfaces abstract in this work we report on a study of entropic threshold of digital speckle patterns images produced by rough surfaces using tsallis entropy the speckle pattern images were obtained in the diffraction plane at the normal direction and they are the outcome of the incidence of a laser beam in the rough metallic surfaces the speckle pattern images were segmented in order to verify the sensitivity of the optimal tsallis entropic threshold value as a function of the surface roughness we show that the surface roughness can be sensed and tuned by this method

model predictive control for want of a local control lyapunov function all is not lost we present stability results for unconstrained discrete time nonlinear systems controlled using finite horizon model predictive control mpc algorithms that do not require the terminal cost to be a local control lyapunov function the two key assumptions we make are that the value function is bounded by a k sub spl infin function of a state measure related to the distance of the state to the target set and that this measure is detectable from the stage cost we show that these assumptions are sufficient to guarantee closed loop asymptotic stability that is semiglobal and practical in the horizon length and robust to small perturbations if the assumptions hold with linear or locally linear k sub spl infin functions then the stability will be global or semiglobal for long enough horizon lengths in the global case we give an explicit formula for a sufficiently long horizon length we relate the upper bound assumption to exponential and asymptotic controllability using terminal and stage costs that are controllable to zero with respect to a state measure we can guarantee the required upper bound but we also require that the state measure be detectable from the stage cost to ensure stability while such costs and state measures may not be easy to construct in general we explore a class of systems called homogeneous systems for which it is straightforward to choose them in fact we show for homogeneous systems that the associated k sub spl infin functions are linear thereby guaranteeing global asymptotic stability we discuss two examples found elsewhere in the mpc literature including the discrete time nonholonomic integrator to demonstrate our methods for these systems we give a new result they can be globally asymptotically stabilized by a finite horizon mpc algorithm that has guaranteed robustness we also show that stable linear systems with control constraints can be globally exponentially stabilized using finite horizon mpc without requiring the terminal cost to be a global control lyapunov function

quantitative approach to multifractality induced by correlations and broad distribution of data abstract we analyze quantitatively the effect of spurious multifractality induced by the presence of fat tailed symmetric and asymmetric probability distributions of fluctuations in time series in the presented approach different kinds of symmetric and asymmetric broad probability distributions of synthetic data are examined starting from levy regime up to those with finite variance we use nonextensive tsallis statistics to construct all considered data in order to have good analytical description of frequencies of fluctuations in the whole range of their magnitude and simultaneously the full control over exponent of power law decay for tails of probability distribution the semi analytical compact formulas are then provided to express the level of spurious multifractality generated by the presence of fat tails in terms of tsallis parameter q and the scaling exponent of the asymptotic decay of cumulated probability density function cdf the results are presented in hurst and holder languages more often used in study of multifractal phenomena according to the provided semi analytical relations it is argued how one can make a clear quantitative distinction for any real data between true multifractality caused by the presence of nonlinear correlations spurious multifractality generated by fat tailed shape of distributions eventually with their asymmetry and the correction due to linear autocorrelations in analyzed time series of finite length in particular the spurious multifractal effect of fat tails is found basic for proper quantitative estimation of all spurious multifractal effects examples from stock market data are presented to support these findings

fractional nonlinear diffusion equation solutions and anomalous diffusion abstract we devote this work to investigate the solutions of a generalized diffusion equation which contains spatial fractional derivatives and nonlinear terms the presence of external forces and absorbent terms is also considered the solutions found here can have a compact or long tail behavior and in particular for the last case in the asymptotic limit we relate these solutions to the levy or tsallis distributions in addition from the results presented here a rich class of diffusive processes including normal and anomalous ones can be obtained

boundedness vs unboundedness of a noise linked to tsallis q statistics the role of the overdamped approximation an apparently ideal way to generate continuous bounded stochastic processes is to consider the stochastically perturbed motion of a point of small mass in an infinite potential well under overdamped approximation here however we show that the aforementioned procedure can be fallacious and lead to incorrect results we indeed provide a counter example concerning one of the most employed bounded noises hereafter called tsallis stariolo borland tsb noise which admits the well known tsallis q statistics as stationary density in fact we show that for negative values of the tsallis parameter q corresponding to sufficiently large diffusion coefficient of the stochastic force the motion resulting from the overdamped approximation is unbounded we then investigate the cause of the failure of kramers first type approximation and we formally show that the solutions of the full newtonian non approximated model are bounded following the physical intuition finally we provide a new family of bounded noi

stability analysis of discrete time infinite horizon optimal control with discounted cost we analyze the stability of general nonlinear discrete time systems controlled by an optimal sequence of inputs that minimizes an infinite horizon discounted cost first assumptions related to the controllability of the system and its detectability with respect to the stage cost are made uniform semiglobal and practical stability of the closed loop system is then established where the adjustable parameter is the discount factor stronger stability properties are thereupon guaranteed by gradually strengthening the assumptions next we show that the lyapunov function used to prove stability is continuous under additional conditions implying that stability has a certain amount of nominal robustness the presented approach is flexible and we show that robust stability can still be guaranteed when the sequence of inputs applied to the system is no longer optimal but near optimal we also analyze stability for cost functions in which the importance of the stage cost increases with time opposite to discounting finally we exploit stability to derive new relationships between the optimal value functions of the discounted and undiscounted problems when the latter is well defined

unconstrained model predictive control and suboptimality estimates for nonlinear continuous time systems this paper presents a continuous time version of recent results on unconstrained nonlinear model predictive control mpc schemes based on a controllability assumption and a corresponding infinite dimensional optimization problem performance estimates and stability conditions are derived in terms of the prediction horizon and the sampling time of the mpc controller moreover improved estimates for small sampling times are discussed and a comparison to the application of the discrete time results in a sampled data context is provided