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On The Infinitesimal Generators of Ornstein-Uhlenbeck Processes with Jumps in
 

Summary: On The Infinitesimal Generators of
Ornstein-Uhlenbeck Processes with Jumps in
Hilbert Space
David Applebaum
Probability and Statistics Department,
University of Sheffield,
Hicks Building, Hounsfield Road,
Sheffield, England, S3 7RH
e-mail: D.Applebaum@sheffield.ac.uk
Abstract
We study Hilbert space valued Ornstein-Uhlenbeck processes (Y (t), t
0) which arise as weak solutions of stochastic differential equations of
the type dY = JY + CdX(t) where J generates a C0 semigroup in
the Hilbert space H, C is a bounded operator and (X(t), t 0) is an
H-valued L´evy process. The associated Markov semigroup is of gen-
eralised Mehler type. We discuss an analogue of the Feller property
for this semigroup and explicitly compute the action of its generator
on a suitable space of twice-differentiable functions. We also compare
the properties of the semigroup and its generator with respect to the
mixed topology and the topology of uniform convergence on compacta.

  

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

 

Collections: Mathematics