On some stochastic parabolic differential equations in a Hilbert space

Khairia El-Said El-Nadi

International Journal of Stochastic Analysis, 2005, vol. 2005, 1-7

Abstract:

We consider some stochastic difference partial differential equations of the form d u ( x , t , c ) = L ( x , t , D ) u ( x , t , c ) d t + M ( x , t , D ) u ( x , t − a , c ) d w ( t ) , where L ( x , t , D ) is a linear uniformly elliptic partial differential operator of the second order, M ( x , t , D ) is a linear partial differential operator of the first order, and w ( t ) is a Weiner process. The existence and uniqueness of the solution of suitable mixed problems are studied for the considered equation. Some properties are also studied. A more general stochastic problem is considered in a Hilbert space and the results concerning stochastic partial differential equations are obtained as applications.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:459581

DOI: 10.1155/JAMSA.2005.167

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