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Levy Processes and Stochastic Integrals in Banach Spaces

Summary: L´evy Processes and Stochastic Integrals in
Banach Spaces
David Applebaum,
Probability and Statistics Department,
University of Sheffield,
Hicks Building, Hounsfield Road,
Sheffield, England, S3 7RH
e-mail: D.Applebaum@sheffield.ac.uk
Dedicated to the memory of K.Urbanik
We review infinite divisibility and L´evy processes in Banach spaces
and discuss the relationship with notions of type and cotype. The
L´evy-It^o decomposition is described. Strong, weak and Pettis-style
notions of stochastic integral are introduced and applied to construct
generalised Ornstein-Uhlenbeck processes.
1 Introduction
This review article has several interlocking themes - L´evy processes, geometry
and probability in Banach spaces, stochastic integration, stochastic evolution
equations, Ornstein-Uhlenbeck processes and self-decomposability. We dis-
cuss each of these in turn.


Source: Applebaum, David - Department of Probability and Statistics, University of Sheffield


Collections: Mathematics