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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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

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

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

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

ergodicity stochastic wave equation Malliavin calculus

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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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