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January 2000 On the Cauchy problem for parabolic SPDEs in Hölder classes
R. Mikulevicius
Ann. Probab. 28(1): 74-103 (January 2000). DOI: 10.1214/aop/1019160112

Abstract

We study Cauchy’s problem for certain second-order linear parabolic stochastic differential equation (SPDE)driven by a cylindrical Brownian motion.Considering its solution as a function with values in a probability space and using the methods of deterministic partial differential equations, we establish the existence and uniqueness of a strong solution in Hölder classes.

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R. Mikulevicius. "On the Cauchy problem for parabolic SPDEs in Hölder classes." Ann. Probab. 28 (1) 74 - 103, January 2000. https://doi.org/10.1214/aop/1019160112

Information

Published: January 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1044.60050
MathSciNet: MR1755998
Digital Object Identifier: 10.1214/aop/1019160112

Subjects:
Primary: 60H15
Secondary: 35K15

Keywords: Cauchy problem , Parabolic stochastic partial differential equations

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 1 • January 2000
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