由布朗运动和泊松随机测度驱动的马尔可夫切换倒向随机微分方程

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-01-02 DOI:10.1080/17442508.2014.914514

Jingtao Shi, Zhen Wu

{"title":"由布朗运动和泊松随机测度驱动的马尔可夫切换倒向随机微分方程","authors":"Jingtao Shi, Zhen Wu","doi":"10.1080/17442508.2014.914514","DOIUrl":null,"url":null,"abstract":"This paper is concerned with backward stochastic differential equations with Markov switching driven by Brownian motion and Poisson random measure. The motivation is a constrained stochastic Riccati equation derived from a stochastic linear quadratic optimal control problem with both Poisson and Markovian jumps. The existence and uniqueness of an adapted solution under global Lipschitz condition on the generator is obtained. The continuous dependence of the solution on parameters is proved. Two comparison theorems are also derived by a generalized Girsanov transformation theorem.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2015-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Backward stochastic differential equations with Markov switching driven by Brownian motion and Poisson random measure\",\"authors\":\"Jingtao Shi, Zhen Wu\",\"doi\":\"10.1080/17442508.2014.914514\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper is concerned with backward stochastic differential equations with Markov switching driven by Brownian motion and Poisson random measure. The motivation is a constrained stochastic Riccati equation derived from a stochastic linear quadratic optimal control problem with both Poisson and Markovian jumps. The existence and uniqueness of an adapted solution under global Lipschitz condition on the generator is obtained. The continuous dependence of the solution on parameters is proved. Two comparison theorems are also derived by a generalized Girsanov transformation theorem.\",\"PeriodicalId\":49269,\"journal\":{\"name\":\"Stochastics-An International Journal of Probability and Stochastic Processes\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2015-01-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Stochastics-An International Journal of Probability and Stochastic Processes\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1080/17442508.2014.914514\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastics-An International Journal of Probability and Stochastic Processes","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/17442508.2014.914514","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 5

摘要

研究了由布朗运动和泊松随机测度驱动的马尔可夫切换倒向随机微分方程。动机是一个约束随机Riccati方程，该方程由一个具有泊松和马尔可夫跳变的随机线性二次最优控制问题导出。得到了发生器在全局Lipschitz条件下的自适应解的存在唯一性。证明了解对参数的连续依赖。利用广义的格萨诺夫变换定理，导出了两个比较定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Backward stochastic differential equations with Markov switching driven by Brownian motion and Poisson random measure

This paper is concerned with backward stochastic differential equations with Markov switching driven by Brownian motion and Poisson random measure. The motivation is a constrained stochastic Riccati equation derived from a stochastic linear quadratic optimal control problem with both Poisson and Markovian jumps. The existence and uniqueness of an adapted solution under global Lipschitz condition on the generator is obtained. The continuous dependence of the solution on parameters is proved. Two comparison theorems are also derived by a generalized Girsanov transformation theorem.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Stochastics-An International Journal of Probability and Stochastic Processes MATHEMATICS, APPLIED-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastics: An International Journal of Probability and Stochastic Processes is a world-leading journal publishing research concerned with stochastic processes and their applications in the modelling, analysis and optimization of stochastic systems, i.e. processes characterized both by temporal or spatial evolution and by the presence of random effects. Articles are published dealing with all aspects of stochastic systems analysis, characterization problems, stochastic modelling and identification, optimization, filtering and control and with related questions in the theory of stochastic processes. The journal also solicits papers dealing with significant applications of stochastic process theory to problems in engineering systems, the physical and life sciences, economics and other areas. Proposals for special issues in cutting-edge areas are welcome and should be directed to the Editor-in-Chief who will review accordingly. In recent years there has been a growing interaction between current research in probability theory and problems in stochastic systems. The objective of Stochastics is to encourage this trend, promoting an awareness of the latest theoretical developments on the one hand and of mathematical problems arising in applications on the other.