{"title":"Invariant measures and boundedness in the mean for stochastic equations driven by Lévy noise","authors":"B. Maslowski, O. Týbl","doi":"10.1142/s0219493722400196","DOIUrl":null,"url":null,"abstract":"Existence of invariant measures and average stability in the mean are studied for stochastic differential equations driven by Lévy process. In particular, some natural conditions are found that verify stabilization of the equation (in the sense of the existence of invariant measures) by jump noise terms. These conditions are verified in several examples.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2022-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastics and Dynamics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219493722400196","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 1
Abstract
Existence of invariant measures and average stability in the mean are studied for stochastic differential equations driven by Lévy process. In particular, some natural conditions are found that verify stabilization of the equation (in the sense of the existence of invariant measures) by jump noise terms. These conditions are verified in several examples.
期刊介绍：
This interdisciplinary journal is devoted to publishing high quality papers in modeling, analyzing, quantifying and predicting stochastic phenomena in science and engineering from a dynamical system''s point of view.
Papers can be about theory, experiments, algorithms, numerical simulation and applications. Papers studying the dynamics of stochastic phenomena by means of random or stochastic ordinary, partial or functional differential equations or random mappings are particularly welcome, and so are studies of stochasticity in deterministic systems.
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