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

DOI:
https://doi.org/10.1090/S0002-9939-10-10230-5

Published electronically:
January 14, 2010

MathSciNet review:
2596056

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-10-10230-5

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