Wiener integrals with respect to the Hermite random field and applications to the wave equation

Jorge Clarke de La Cerda (1) , Ciprian A. Tudor (2)

1 Departamento de Matemática, Universidad del Bío-Bío
2 LPP - Laboratoire Paul Painlevé - UMR 8524

The Hermite random field has been introduced as a limit of some weighted Hermite variations of the fractional Brownian sheet. In this work we define it as a multiple integral with respect to the standard Brownian sheet and introduce Wiener integrals with respect to it. As an application we study the wave equation driven by the Hermite sheet. We prove the existence of the solution and we study the regularity of its sample paths, the existence of the density and of its local times. 2000 AMS Classification Numbers: 60F05, 60H05, 60G18.

Mots clés: Wiener integral; Hermite process; Hermite sheet; Stochastic wave equation

Domaines: Probabilités [math.PR]

Jorge Clarke de La Cerda, Ciprian A. Tudor. Wiener integrals with respect to the Hermite random field and applications to the wave equation. Collectanea Mathematica, 2014, 65, pp.341 - 356. ⟨10.1007/s13348-014-0108-9⟩. ⟨hal-01393678⟩