Stochastic Partial Differential Equations with LГ©vy Noise: An Evolution Equation Approach

✍ Scribed by Peszat S., Zabczyk J.

• Publisher: Cambridge University Press
• Year: 2007
• Tongue: English
• Leaves: 432
• Series: Encyclopedia of Mathematics and its Applications
• Edition: 1
• Category: Library

✦ Synopsis

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 LГ©vy processes in infinite dimensions and their reproducing kernel Hilbert spaces; cylindrical LГ©vy 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