Strong solutions of SDES with singular drift and Sobolev diffusion coefficients

Xicheng Zhang

doi:10.1016/j.spa.2005.06.003

Strong solutions of SDES with singular drift and Sobolev diffusion coefficients

Xicheng Zhang^*

^*Corresponding author for this work

Huazhong University of Science and Technology

Research output: Contribution to journal › Article › peer-review

79 Citations (Scopus)

Abstract

In this paper we prove the existence of a unique strong solution up to the explosion time for an SDE with a uniformly non-degenerate Sobolev diffusion coefficient (non-Lipschtiz) and locally integrable drift coefficient. Moreover, two non-explosion conditions are given.

Original language	English
Pages (from-to)	1805-1818
Number of pages	14
Journal	Stochastic Processes and their Applications
Volume	115
Issue number	11
DOIs	https://doi.org/10.1016/j.spa.2005.06.003
Publication status	Published - Nov 2005
Externally published	Yes

Keywords

Krylov's estimate
Sobolev space
Strong solution
Zvonkin's transformation

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10.1016/j.spa.2005.06.003

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title = "Strong solutions of SDES with singular drift and Sobolev diffusion coefficients",

abstract = "In this paper we prove the existence of a unique strong solution up to the explosion time for an SDE with a uniformly non-degenerate Sobolev diffusion coefficient (non-Lipschtiz) and locally integrable drift coefficient. Moreover, two non-explosion conditions are given.",

keywords = "Krylov's estimate, Sobolev space, Strong solution, Zvonkin's transformation",

author = "Xicheng Zhang",

year = "2005",

month = nov,

doi = "10.1016/j.spa.2005.06.003",

language = "English",

volume = "115",

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T1 - Strong solutions of SDES with singular drift and Sobolev diffusion coefficients

AU - Zhang, Xicheng

PY - 2005/11

Y1 - 2005/11

N2 - In this paper we prove the existence of a unique strong solution up to the explosion time for an SDE with a uniformly non-degenerate Sobolev diffusion coefficient (non-Lipschtiz) and locally integrable drift coefficient. Moreover, two non-explosion conditions are given.

AB - In this paper we prove the existence of a unique strong solution up to the explosion time for an SDE with a uniformly non-degenerate Sobolev diffusion coefficient (non-Lipschtiz) and locally integrable drift coefficient. Moreover, two non-explosion conditions are given.

KW - Krylov's estimate

KW - Sobolev space

KW - Strong solution

KW - Zvonkin's transformation

UR - http://www.scopus.com/inward/record.url?scp=25644446084&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2005.06.003

DO - 10.1016/j.spa.2005.06.003

M3 - Article

AN - SCOPUS:25644446084

SN - 0304-4149

VL - 115

SP - 1805

EP - 1818

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 11

ER -

Strong solutions of SDES with singular drift and Sobolev diffusion coefficients

Abstract

Keywords

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