Hitting properties and non-uniqueness for SDEs driven by stable processes

被引：4

作者：

Berestycki, J. ^{[1
]}

Doering, L. ^{[1
]}

Mytnik, L. ^{[2
]}

Zambotti, L. ^{[1
]}

机构：

[1] Univ Paris 06, Lab Probabilites & Modeles Aleatoires, F-75252 Paris 05, France

[2] Technion Israel Inst Technol, Fac Ind Engn & Management, IL-32000 Haifa, Israel

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2015年 / 125卷 / 03期

基金：

以色列科学基金会;

关键词：

Continuous state branching processes; Immigration; Self-similarity; Jump-diffusion; STOCHASTIC DIFFERENTIAL-EQUATIONS; SIMILAR MARKOV-PROCESSES; PATHWISE UNIQUENESS; RECURRENT EXTENSIONS; LEVY PROCESSES;

D O I：

10.1016/j.spa.2014.10.012

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study a class of self-similar jump type SDEs driven by Holder continuous drift and noise coefficients. Using the Lamperti transformation for positive self-similar Markov processes we obtain a necessary and sufficient condition for almost sure extinction in finite time. We then show that in some cases pathwise uniqueness holds in a restricted sense, namely among solutions spending a Lebesgue-negligible amount of time at 0. A direct power transformation plays a key role. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：918 / 940

页数：23

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