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Stochastic Integration in Banach Spaces
Theory and Applications
Langbeschreibung
Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces.
Inhaltsverzeichnis
1.Introduction.- 2.Preliminaries.- 3.Stochastic Integrals with Respect to Compensated Poisson Random Measures.- 4.Stochastic Integral Equations in Banach Spaces.- 5.Stochastic Partial Differential Equations in Hilbert Spaces.- 6.Applications.- 7.Stability Theory for Stochastic Semilinear Equations.- A Some Results on compensated Poisson random measures and stochastic integrals.- References.- Index.
Professor Vidyadhar Mandrekar is an expert in stochastic differential equations in infinite dimensional spaces and filtering. In addition he has advised doctoral students in financial mathematics and water flows. He is the first recipient of the Distinguished Faculty Award in the Department of Statistics and Probability at Michigan State University. Professor Barbara Rüdiger graduated at the University Roma "Tor Vergata" in Mathematics with Mathematical Physics. She moved to Germany with an individual European Marie Curie "Training and Mobility of Researchers" fellowship in 1997, where she became an expert in stochastic differential equations in infinite dimensional spaces, also with non-Gaussian noise, which she applies in different areas. She is the Chair of the stochastic group at the University of Wuppertal.
ISBN-13:
9783319128535
Veröffentl:
2014
Seiten:
211
Autor:
Vidyadhar Mandrekar
Serie:
73, Probability Theory and Stochastic Modelling
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
28,88 €*
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