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P-th moment growth bounds of infinite-dimensional stochastic evolution equations

Published online by Cambridge University Press:  14 November 2011

Kai Liu
Kai Liu
Affiliation:
Department of Statistics and Modelling Science, University of Strathclyde, Glasgow Gl 1XH, Scotland, U.K. e-mail: [email protected]
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Extract

The aim of this paper is to investigate the p-th moment growth bounds wilh a general rate function λ(t) of the strong solution for a class of stochastic differential equations in infinite dimensional space under various sufficient hypotheses. The results derived here extend the usual situations to some extent, containing for example the polynomial or iterated logarithmic growth cases studied by many authors. In particular, more generalised sufficient conditions, ensuring the p-th moment upper-bound of sample paths given by solutions of a class of nonlinear stochastic evolution equations, are captured. Applications to parabolic itô equations are also considered.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 1 , 1998 , pp. 107 - 121
Copyright
Copyright © Royal Society of Edinburgh 1998

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