The Annals of Probability

On the Cauchy problem for parabolic SPDEs in Hölder classes

R. Mikulevicius

Full-text: Open access

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.

Article information

Source
Ann. Probab., Volume 28, Number 1 (2000), 74-103.

Dates
First available in Project Euclid: 18 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1019160112

Digital Object Identifier
doi:10.1214/aop/1019160112

Mathematical Reviews number (MathSciNet)
MR1755998

Zentralblatt MATH identifier
1044.60050

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 35K15: Initial value problems for second-order parabolic equations

Keywords
Parabolic stochastic partial differential equations Cauchy problem

Citation

Mikulevicius, R. On the Cauchy problem for parabolic SPDEs in Hölder classes. Ann. Probab. 28 (2000), no. 1, 74--103. doi:10.1214/aop/1019160112. https://projecteuclid.org/euclid.aop/1019160112


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