Summary: L´evy Processes and Stochastic Integrals in
Probability and Statistics Department,
University of Sheffield,
Hicks Building, Hounsfield Road,
Sheffield, England, S3 7RH
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.
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.