Non-central limit theorem for the spatial average of the solution to the wave equation with Rosenblatt noise

DOI10.1090/tpms/1167zbMath1495.60056OpenAlexW4281285430WikidataQ113822483 ScholiaQ113822483MaRDI QIDQ5080407

Rémi Dhoyer, Ciprian A. Tudor

Publication date: 31 May 2022

Published in: Theory of Probability and Mathematical Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/tpms/1167

zbMATH Keywords

cumulantsmultiple stochastic integralsstochastic wave equationRosenblatt sheetsecond Wiener chaos

Mathematics Subject Classification ID

Gaussian processes (60G15) Central limit and other weak theorems (60F05) Stochastic calculus of variations and the Malliavin calculus (60H07) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Cites Work

• Wiener integrals with respect to the Hermite random field and applications to the wave equation
• A central limit theorem for the stochastic wave equation with fractional noise
• Spatial ergodicity of stochastic wave equations in dimensions 1, 2 and 3
• Gaussian fluctuations for the stochastic heat equation with colored noise
• A central limit theorem for the stochastic heat equation
• Analysis of Variations for Self-similar Processes
• Normal Approximations with Malliavin Calculus
• The Malliavin Calculus and Related Topics
• The linear stochastic heat equation with Hermite noise
• Spatial average for the solution to the heat equation with Rosenblatt noise
• Wiener Integrals with Respect to the Hermite Process and a Non-Central Limit Theorem
• Unnamed Item

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