Frontiers of Mathematics in China >

2011 , Vol. 6 >Issue 1: 129 - 136

DOI: https://doi.org/10.1007/s11464-010-0083-8

RESEARCH ARTICLE

Pathwise uniqueness of multi-dimensional stochastic differential equations with Hölder diffusion coefficients

  • Dejun LUO
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  • Key Lab of Random Complex Structures and Data Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Received date: 07 Apr 2010

Accepted date: 28 Aug 2010

Published date: 01 Feb 2011

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

We extend Yamada-Watababe’s criterion [J. Math. Kyoto Univ., 1971, 11: 553-563] on the pathwise uniqueness of one-dimensional stochastic differential equations to a special class of multi-dimensional stochastic differential equations.

Key words： Stochastic differential equation (SDE); strong solution; pathwise uniqueness; Hölder continuity

Cite this article

Dejun LUO . Pathwise uniqueness of multi-dimensional stochastic differential equations with Hölder diffusion coefficients[J]. Frontiers of Mathematics in China, 2011 , 6(1) : 129 -136 . DOI: 10.1007/s11464-010-0083-8

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
Dawson D A, Fleischmann K, Xiong J. Strong uniqueness for cyclically symbiotic branching diffusions. Statist Probab Lett, 2005, 73: 251-257

DOI

2
Fang S. Canonical Brownian motion on the diffeomorphism group of the circle. J Funct Anal, 2002, 196: 162-179

DOI

3
Fang S, Imkeller P, Zhang T. Global flows for stochastic differential equations without global Lipschitz conditions. Ann of Probab, 2007, 35: 180-205

DOI

4
Fang S, Luo D. Flow of homeomorphisms and stochastic transport equations. Stoch Anal Appl, 2007, 25: 1079-1108

DOI

5
Fang S, Luo D, Thalmaier A. Stochastic differential equations with coefficients in Sobolev spaces. J Funct Anal, 2010, 259: 1129-1168

DOI

6
Fang S, Zhang T. A study of a class of differential equations with non-Lipschitzian coefficients. Probab Theory Relat Fields, 2005, 132: 356-390

DOI

7
Fang S, Zhang T. Isotropic stochastic flow of homeomorphisms on Sd for the critical Sobolev exponent. J Math Pures et Appl, 2006, 85: 580-597

DOI

8
He H. Strong uniqueness for a class of singular SDEs for catalytic branching diffusions. Statist Probab Lett, 2009, 79: 182-187

DOI

9
Ikeda N, Watanabe S. Stochastic Differential Equations and Diffusion Processes.2nd ed. North-Holland Mathematical Library, Vol 24.Amsterdam: North-Holland, 1989

10
Krylov N V, Röckner M. Strong solutions of stochastic equations with singular time dependent drift. Prob Theory Relat Fields, 2005, 131: 154-196

DOI

11
Kunita H. Stochastic Flows and Stochastic Differential Equations.Cambridge: Cambridge University Press, 1990

12
Luo D. Regularity of solutions to differential equations with non-Lipschitz coefficients. Bull Sci Math, 2008, 132: 257-271

DOI

13
Malliavin P. The canonical diffusion above the diffeomorphism group of the circle. C R Acad Sci, 1999, 329: 325-329

14
Suresh Kumar K. A class of degenerate stochastic differential equations with non-Lipschitz coefficients.http://arxiv.org/abs/0904.2629

15
Yamada T, Watanabe S. On the uniqueness of stochastic differential equations. J Math Kyoto Univ, 1971, 11: 553-563

16
Zhang X. Homeomorphic flows for multi-dimensional SDEs with non-Lipschitz coefficients. Stochastic Process Appl, 2005, 115: 435-448; Erratum to “Homeomorphic flows for multi-dimensional SDEs with non-Lipschitz coefficients”. Stochastic Process Appl, 2006, 116: 873-875

DOI

17
Zhang X. Strong solutions of SDEs with singular drift and Sobolev diffusion coefficients. Stochastic Process Appl, 2005, 115: 1805-1818

DOI

18
Zhang X. Stochastic flows of SDEs with irregular coefficients and stochastic transport equations. Bull Sci Math, 2010, 134: 340-378

DOI

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