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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:111

Article

Bass, RF ; Burdzy, K ; Chen, ZQ

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

DOI  :  10.1016/j.spa.2004.01.010

来源: Elsevier

【 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.

【 授权许可】

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