SPDEs with -Stable Lévy Noise: A Random Field Approach

Raluca M. Balan

International Journal of Stochastic Analysis, 2014, vol. 2014, 1-22

Abstract:

This paper is dedicated to the study of a nonlinear SPDE on a bounded domain in , with zero initial conditions and Dirichlet boundary, driven by an -stable Lévy noise with , , and possibly nonsymmetric tails. To give a meaning to the concept of solution, we develop a theory of stochastic integration with respect to this noise. The idea is to first solve the equation with “truncated†noise (obtained by removing from the jumps which exceed a fixed value ), yielding a solution , and then show that the solutions coincide on the event , for some stopping times converging to infinity. A similar idea was used in the setting of Hilbert-space valued processes. A major step is to show that the stochastic integral with respect to satisfies a th moment inequality. This inequality plays the same role as the Burkholder-Davis-Gundy inequality in the theory of integration with respect to continuous martingales.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:793275

DOI: 10.1155/2014/793275

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