Stochastic differential equations driven by stable processes for which pathwise uniqueness fails

被引：31

作者：

Bass, RF

Burdzy, K

Chen, ZQ

机构：

[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

[2] Univ Washington, Dept Math, Seattle, WA 98115 USA

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2004年 / 111卷 / 01期

基金：

美国国家科学基金会;

关键词：

stable processes; pathwise uniqueness; stochastic differential equations; time change; crossing estimates;

D O I：

10.1016/j.spa.2004.01.010

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：

Let Z, be a one-dimensional symmetric stable process of order alpha with alpha is an element of (0, 2) and consider the stochastic differential equation d X-t = phi(X-t-) dZ(t). For beta < (1/alpha) Lambda 1, we show there exists a function phi that is bounded above and below by positive constants and which is Holder continuous of order beta but for which pathwise uniqueness of the stochastic differential equation does not hold. This result is sharp. (C) 2004 Elsevier B.V. All rights reserved.

引用

页码：1 / 15

页数：15

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