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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Stability in distribution of mild solutions to stochastic partial differential equations


Authors: Jianhai Bao, Zhenting Hou and Chenggui Yuan
Journal: Proc. Amer. Math. Soc. 138 (2010), 2169-2180
MSC (2010): Primary 60H15, 60H30
Published electronically: January 14, 2010
MathSciNet review: 2596056
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Abstract: In the present paper, we investigate stochastic partial differential equations. By introducing a suitable metric between the transition probability functions of mild solutions, we derive sufficient conditions for stability in distribution of mild solutions. Consequently, we generalize some existing results to infinite dimensional cases. Finally, one example is constructed to demonstrate the applicability of our theory.


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Additional Information

Jianhai Bao
Affiliation: School of Mathematics, Central South University, Changsha, Hunan 410075, People’s Republic of China

Zhenting Hou
Affiliation: School of Mathematics, Central South University, Changsha, Hunan 410075, People’s Republic of China

Chenggui Yuan
Affiliation: Department of Mathematics, Swansea University, Swansea SA2 8PP, United Kingdom
Email: C.Yuan@Swansea.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10230-5
PII: S 0002-9939(10)10230-5
Keywords: Stochastic partial differential equation, mild solution, stability in distribution
Received by editor(s): March 16, 2009
Received by editor(s) in revised form: September 23, 2009, and September 24, 2009
Published electronically: January 14, 2010
Additional Notes: This work was partially supported by the NNSF of China (Grant No. 10671212)
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2010 American Mathematical Society