On stochastic evolution equations with state-dependent diffusion terms

Jai Heui Kim; Jung Hoon Song

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 1997; 34(4): 1019-1028

Printed December 1, 1997

On stochastic evolution equations with state-dependent diffusion terms

Jai Heui Kim and Jung Hoon Song

Pusan National University and Pusan National University

Abstract

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Abstract

The integral solution for a deterministic evolution equation was introduced by Benilan. Similarly, in this paper, we define the integral solution for a stochastic evolution equation with a state-dependent diffusion term and prove that there exists a unique integral solution of the stochastic evolution equation under some conditions for the coefficients. Moreover we prove that this solution is a unique strong solution.

Keywords: stochastic evolution equation, integral solution

MSC numbers: 60H10