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  3. Stochastic Partial Differential Equations with Lévy Noise
  • Cited by 335
Publisher:
Cambridge University Press
Online publication date:
November 2010
Print publication year:
2007
Online ISBN:
9780511721373
DOI:
https://doi.org/10.1017/CBO9780511721373
Subjects:
Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Probability Theory and Stochastic Processes, Statistics and Probability
Series:
Encyclopedia of Mathematics and its Applications (113)
Information

Book description

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 Lévy processes in infinite dimensions and their reproducing kernel Hilbert spaces; cylindrical Lévy 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.

Reviews

'Summarising, this book is an excellent addition to the literature on stochastic partial differential equations in general and in particular with respect to evolution equations driven by a discontinuous noise. The exposition is self-contained and very well written and, in my opinion, will become a standard tool for everyone working on stochastic evolution equations and related areas.'

Source: Zentralblatt MATH

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