Electronic Journal of Probability

Stochastic evolution equations with multiplicative noise

Tijana Levajković, Stevan Pilipović, Dora Seleši, and Milica Žigić

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Abstract

We study parabolic stochastic partial differential equations(SPDEs), driven by two types of operators: one linear closedoperator generating a $C_0-$semigroup and one linear boundedoperator with Wick-type multiplication, all of them set in theinfinite dimensional space framework of white noise analysis. Weprove existence and uniqueness of solutions for this class of SPDEs.In particular, we also treat the stationary case when thetime-derivative is equal to zero.

Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 19, 23 pp.

Dates
Accepted: 28 February 2015
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465067125

Digital Object Identifier
doi:10.1214/EJP.v20-3696

Mathematical Reviews number (MathSciNet)
MR3317161

Zentralblatt MATH identifier
1321.60137

Subjects
Primary: 60H30: Applications of stochastic analysis (to PDE, etc.)
Secondary: 60H40: White noise theory 60G20: Generalized stochastic processes 60H07: Stochastic calculus of variations and the Malliavin calculus 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 46N30: Applications in probability theory and statistics

Keywords
generalized stochastic process chaos expansion stochastic evolution equation Wick product white noise $C_0-$semigroup infinitesimal generator stochastic operator

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Levajković, Tijana; Pilipović, Stevan; Seleši, Dora; Žigić, Milica. Stochastic evolution equations with multiplicative noise. Electron. J. Probab. 20 (2015), paper no. 19, 23 pp. doi:10.1214/EJP.v20-3696. https://projecteuclid.org/euclid.ejp/1465067125


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