随机微分-差分混合系统的存在性和唯一性定理

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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