Limit Theory for Stochastic Difference Equations
Some new finite difference inequalities arising in the theory of difference equations
... Finite difference inequalities in one or two independent variables which provide expli- cit bounds play a fundamental role in the study of boundedness, uniqueness, and con- tinuous dependence on initial data of ...
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Asymptotic Constancy in Linear Difference Equations: Limit Formulae and Sharp Conditions
... It is found that every solution of a system of linear delay difference equations has finite limit at infinity, if some conditions are satisfied. These are much weaker than the known sufficient conditions for ...
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On the local dynamics of polynomial difference equations with fading stochastic perturbations
... when lim n→∞ X n (ω) = 0, since (1) does not have an equilibrium solution at zero. However, we persist in using this nomenclature for two reasons. First, we are investigating the effect of noisy input on the dynamics of ...
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Finite difference schemes for linear stochastic integro-differential equations
... Abstract We study the rate of convergence of an explicit and an implicit-explicit finite dif- ference scheme for linear stochastic integro-differential equations of parabolic type arising in non-linear ...
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Global asymptotic stability of solutions of cubic stochastic difference equations
... CUBIC STOCHASTIC DIFFERENCE EQUATIONS ALEXANDRA RODKINA AND HENRI SCHURZ Received 18 September 2003 and in revised form 22 December 2003 Global almost sure asymptotic stability of solutions of some ...
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Stability of Equilibrium Points of Fractional Difference Equations with Stochastic Perturbations
... additive stochastic perturbations type of σ x n − xξ n1 that are directly proportional to the deviation of the system state x n from the equilibrium point ...the theory of stability of stochastic ...
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On almost sure asymptotic periodicity for scalar stochastic difference equations
... difference equations. Stochastic difference equations have been studied intensively during the last ...to stochastic difference equations and stabilisation see ...nonlinear ...
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A Study on Properties of Regularity for Fractional Difference Equations in Stochastic Processes
... Abstract- In this paper, we present some results for vector-valued fractional difference equations. We are successful to completely characterize the maximal regularity of solutions for the problem in ...
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Mathematical framework for pseudo-spectra of linear stochastic difference equations
... 28049 Madrid, Spain. Abstract Although spectral analysis of stationary stochastic processes has solid mathematical foundations, this is not always so for some non-stationary cases. Here, we establish a rigorous ...
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Stochastic evolution as a quasiclassical limit of a boundary value problem for Schrödinger equations
... linear stochastic, quantum stochastic and even deterministic equations in Banach ...these equations (in particu- lar those decribing the processes of continuous quantum measurements) are ...
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Nevanlinna theory for the q-difference operator and meromorphic solutions of q-difference equations
... q-difference equations in Section ...Nevanlinna theory, and give an outline of how it can be used to analyze the value distribution of zero-order meromorphic ...q-difference equations ...
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Attracting and quasi invariant sets for a class of impulsive stochastic difference equations
... Abstract The aim of this article is to study the attracting and quasi-invariant sets for a class of impulsive stochastic difference equations. By establishing a difference inequality, we ...
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On the oscillation of solutions for a class of second order nonlinear stochastic difference equations
... the theory established, we also give a sufficient criterion on the almost sure oscillation of solutions for a class of second-order stochastic difference equation of neutral ...
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Finite Difference Schemes for Stochastic Partial Differential Equations in Sobolev Spaces
... finite difference approximations for the solutions of parabolic ...for equations with such data we get dimension-invariant conditions on the smoothness of the ...
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Solution of Stochastic Non Homogeneous Linear First Order Difference Equations
... in difference equations for a number of ...example, difference equations frequently arise while determining the cost of an algorithm in big-O notation ...engineering, difference ...
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Analysis of an asymptotic preserving scheme for stochastic linear kinetic equations in the diffusion limit
... words. stochastic transport equations, diffusion limit, asymptotic preserving scheme, stiff terms, stability analysis 1 Introduction In the physical contexts associated with neutron transport, ...
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Fast-Diffusion Limit with Large Noise for Systems of Stochastic Reaction-Diffusion Equations
... The reminder of this paper is organized as follows. In Section 2 we state the precise setting for equation (1) and the assumptions that we need. In Section 3 we derive the fast-diffusion limit with error and ...
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Problems in limit theory for martingales and posterior distributions from stochastic processes
... tending a result of Heyde, we show however, that the tail sum of squares norming yields CLT's in more general situations than the Bayesian norming; and provide appropriate examples. Sufficient conditions for the ...
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Theory of nth order linear general quantum difference equations
... difference equations based on the general quantum difference operator D β which is defined by D β f (t) = (f( β (t)) – f(t))/( β (t) – t), β (t) = t, where β is a strictly increasing continuous function defined on an ...
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Finite Difference Approximation for Linear Stochastic Partial Differential Equations with Method of Lines
... A stochastic partial differential equation, or SPDE, describes the dynamics of a stochastic process de fi ned on a space-time ...differential equations (ODEs) by discretizing the spatial dimension of ...
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