The cutoff phenomenon for the stochastic heat and wave equation subject to small Lévy noise

• Published in: Stochastic partial differential equations : analysis and computations Vol. 11; no. 3; pp. 1164 - 1202
• Main Authors: Barrera, Gerardo, Högele, Michael A., Pardo, Juan Carlos
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.09.2023; Springer Nature B.V
• Subjects: Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Mathematics; Mathematics and Statistics; Numerical Analysis; Partial Differential Equations; Probability Theory and Stochastic Processes; Statistical Theory and Methods; Thermodynamics; Wave equations; 47D06; Error estimates; Stochastic partial differential equations; 37A30; 60G51; Exponential ergodicity; Wasserstein distance; Heat semigroup; Infinite dimensional Ornstein–Uhlenbeck processes; Lévy processes; 60H15; The cutoff phenomenon
• ISSN: 2194-0401; 2194-041X
• DOI: 10.1007/s40072-022-00257-7

This article generalizes the small noise cutoff phenomenon obtained recently by Barrera, Högele and Pardo (JSP2021) to the mild solutions of the stochastic heat equation and the damped stochastic wave equation over a bounded domain subject to additive and multiplicative Wiener and Lévy noises in the Wasserstein distance. The methods rely on the explicit knowledge of the respective eigensystem of the stochastic heat and wave operator and the explicit representation of the multiplicative stochastic solution flows in terms of stochastic exponentials.