The spatial sojourn time for the solution to the wave equation with moving time: Central and non-central limit theorems

Ciprian A. Tudor and Jérémy Zurcher

Stochastic Processes and their Applications, 2024, vol. 172, issue C

Abstract: We consider the sojourn time of the solution to the stochastic wave equation with space–time white noise on the spatial domain [−T,T]. We analyze its asymptotic behavior in distribution when T→∞ and the time variable also tends to infinity with T, i.e.t=Tα with α>0. For α<1, we prove that the properly renormalized sojourn time satisfies a Central Limit Theorem and we derive its rate of convergence under the Wasserstein distance by using the techniques of the Stein–Malliavin calculus. When the time exceeds the critical value t=T, we show that the renormalized sojourn time converges in law to a non-Gaussian limit.

Keywords: Sojoun time; Stochastic wave equation; Multiple Wiener–Itô integrals; Stein–Malliavin calculus (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104333

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