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

Richard F. Bass; Krzysztof Burdzy; Zhen Qing Chen

doi:10.1016/j.spa.2004.01.010

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

Richard F. Bass^*, Krzysztof Burdzy, Zhen Qing Chen

^*此作品的通讯作者

科研成果: 期刊稿件 › 文章 › 同行评审

27 引用（Scopus）

摘要

Let Z_t be a one-dimensional symmetric stable process of order α with α∈(0,2) and consider the stochastic differential equation dX_t=φ(X_t-)dZ_t. 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.

源语言	英语
页（从-至）	1-15
页数	15
期刊	Stochastic Processes and their Applications
卷	111
期	1
DOI	https://doi.org/10.1016/j.spa.2004.01.010
出版状态	已出版 - 5月 2004
已对外发布	是

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Bass, R. F., Burdzy, K., & Chen, Z. Q. (2004). Stochastic differential equations driven by stable processes for which pathwise uniqueness fails. Stochastic Processes and their Applications, 111(1), 1-15. https://doi.org/10.1016/j.spa.2004.01.010

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abstract = "Let Zt be a one-dimensional symmetric stable process of order α with α∈(0,2) and consider the stochastic differential equation dXt=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 H{\"o}lder continuous of order β but for which pathwise uniqueness of the stochastic differential equation does not hold. This result is sharp.",

keywords = "Crossing estimates, Pathwise uniqueness, Stable processes, Stochastic differential equations, Time change",

author = "Bass, {Richard F.} and Krzysztof Burdzy and Chen, {Zhen Qing}",

year = "2004",

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doi = "10.1016/j.spa.2004.01.010",

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T1 - Stochastic differential equations driven by stable processes for which pathwise uniqueness fails

AU - Bass, Richard F.

AU - Burdzy, Krzysztof

AU - Chen, Zhen Qing

PY - 2004/5

Y1 - 2004/5

N2 - Let Zt be a one-dimensional symmetric stable process of order α with α∈(0,2) and consider the stochastic differential equation dXt=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.

AB - Let Zt be a one-dimensional symmetric stable process of order α with α∈(0,2) and consider the stochastic differential equation dXt=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.

KW - Crossing estimates

KW - Pathwise uniqueness

KW - Stable processes

KW - Stochastic differential equations

KW - Time change

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U2 - 10.1016/j.spa.2004.01.010

DO - 10.1016/j.spa.2004.01.010

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SN - 0304-4149

VL - 111

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EP - 15

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 1

ER -

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

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