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.
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页码：918 / 940
页数：23
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