Title of article
Stochastic differential equations driven by stable processes for which pathwise uniqueness fails
Author/Authors
Bass، نويسنده , , Richard F. and Burdzy، نويسنده , , Krzysztof and Chen، نويسنده , , Zhen-Qing، نويسنده ,
Issue Information
روزنامه با شماره پیاپی سال 2004
Pages
15
From page
1
To page
15
Abstract
Let Zt be a one-dimensional symmetric stable process of order α with α∈(0,2) and consider the stochastic differential equationdXt=φ(Xt−) dZt.For β<(1/α)∧1, we show there exists a function φ that is bounded above and below by positive constants and which is Hölder continuous of order β but for which pathwise uniqueness of the stochastic differential equation does not hold. This result is sharp.
Keywords
Stable processes , Pathwise uniqueness , Time change , Crossing estimates , stochastic differential equations
Journal title
Stochastic Processes and their Applications
Serial Year
2004
Journal title
Stochastic Processes and their Applications
Record number
1577376
Link To Document