随机微分-差分混合系统的存在性和唯一性定理

IF 0.8 4区数学 Q2 MATHEMATICS Differential Equations Pub Date : 2024-09-11 DOI:10.1134/s0012266124050033

A. A. Levakov, D. A. Dolzhenkova

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引用次数: 0

摘要

摘要随机微分-差分混合系统是一个耦合变量系统，其中一些变量的动力学由随机微分方程描述，另一些变量的动力学由差分方程描述。本文研究了具有两类差分方程的系统：第一类是涉及乘法维纳过程的差分方程，第二类是具有延迟的差分方程。证明了这两种系统的存在性和唯一性定理。系统参数的基本条件是局部 Lipschitz 条件和线性增长阶数。

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Existence and Uniqueness Theorems for Stochastic Differential-Difference Hybrid Systems

Abstract

A stochastic differential-difference hybrid system is a system of coupled variables whose dynamics is described by stochastic differential equations for some of them and difference equations for the others. Systems with two types of difference equations are examined: first, a difference equation in the form of a process involving a multiplicative Wiener process, and second, a difference equation with delay. The existence and uniqueness theorems for both systems are proved. The basic conditions on the system’s parameters are local Lipschitz conditions and linear growth order.

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来源期刊

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.