Stochastic Partial Differential Equations with Levy Noise : An Evolution Equation Approach

Comprehensive monograph detailing evolution equation approach to the solution of stochastic partial differential equations driven by Lévy space-time noise, by two leading international experts. The majority of results appear here for the first time in book form and the volume is sure to stimulate further research in this important field.

Recent years have seen an explosion of interest in stochastic partial differential equations where the driving noise is discontinuous. In this comprehensive monograph, two leading experts detail the evolution equation approach to their solution. Most of the results appeared here for the first time in book form. The authors start with a detailed analysis of Levy processes in infinite dimensions and their reproducing kernel Hilbert spaces; cylindrical Levy processes are constructed in terms of Poisson random measures; stochastic integrals are introduced. Stochastic parabolic and hyperbolic equations on domains of arbitrary dimensions are studied, and applications to statistical and fluid mechanics and to finance are also investigated. Ideal for researchers and graduate students in stochastic processes and partial differential equations, this self-contained text will also interest those working on stochastic modeling in finance, statistical physics and environmental science.