Jump-diffusion processes in random environments

被引：5

作者：

Jakubowski, Jacek ^{[1
,2
]}

Nieweglowski, Mariusz ^{[2
,3
]}

机构：

[1] Univ Warsaw, Inst Math, PL-02097 Warsaw, Poland

[2] Warsaw Univ Technol, Fac Math & Informat Sci, PL-00662 Warsaw, Poland

[3] IIT, Dept Appl Math, Chicago, IL 60616 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2014年 / 257卷 / 07期

关键词：

Jump-diffusion; Stochastic differential equations; Markov switching; STOCHASTIC DIFFERENTIAL-EQUATIONS;

D O I：

10.1016/j.jde.2014.05.052

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we investigate jump-diffusion processes in random environments which are given as the weak solutions of SDEs. We formulate conditions ensuring existence and uniqueness in law of solutions. We investigate the Markov property. To prove uniqueness we solve a general martingale problem for cadlag processes. This result is of independent interest. Application of our results to generalized exponential Levy model are present in the last section. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：2671 / 2703

页数：33

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