{"title":"Existence and Uniqueness Theorems for Stochastic Differential-Difference Hybrid Systems","authors":"A. A. Levakov, D. A. Dolzhenkova","doi":"10.1134/s0012266124050033","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> A stochastic differential-difference hybrid system is a system of coupled variables whose\ndynamics is described by stochastic differential equations for some of them and difference\nequations for the others. Systems with two types of difference equations are examined: first,\na difference equation in the form of a process involving a multiplicative Wiener process, and\nsecond, a difference equation with delay. The existence and uniqueness theorems for both systems\nare proved. The basic conditions on the system’s parameters are local Lipschitz conditions and\nlinear growth order.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124050033","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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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