Electronic Communications in Probability

Spatial ergodicity of stochastic wave equations in dimensions 1, 2 and 3

David Nualart and Guangqu Zheng

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Abstract

In this note, we study a large class of stochastic wave equations with spatial dimension less than or equal to $3$. Via a soft application of Malliavin calculus, we establish that their random field solutions are spatially ergodic.

Article information

Source
Electron. Commun. Probab., Volume 25 (2020), paper no. 80, 11 pp.

Dates
Received: 24 July 2020
Accepted: 6 November 2020
First available in Project Euclid: 9 December 2020

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1607504414

Digital Object Identifier
doi:10.1214/20-ECP361

Mathematical Reviews number (MathSciNet)
MR4187721

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60] 60H07: Stochastic calculus of variations and the Malliavin calculus 37A25: Ergodicity, mixing, rates of mixing

Keywords
ergodicity stochastic wave equation Malliavin calculus

Rights
Creative Commons Attribution 4.0 International License.

Citation

Nualart, David; Zheng, Guangqu. Spatial ergodicity of stochastic wave equations in dimensions 1, 2 and 3. Electron. Commun. Probab. 25 (2020), paper no. 80, 11 pp. doi:10.1214/20-ECP361. https://projecteuclid.org/euclid.ecp/1607504414


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References

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