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

Abstract

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.

arXiv commentThe final publication is available at Springer via http://dx.doi.org/10.1007/s13348-014-0108-9

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Cited by in corpus (4)

• Behavior with respect to the Hurst index of the Wiener Hermite integrals and application to SPDEs
• Functional limit theorems for generalized variations of the fractional Brownian sheet
• Wiener integrals with respect to the two-parameter tempered Hermite random fields
• Sample path properties of multidimensional integral with respect to stochastic measure