MATHEMATICS COLLOQUIUM

 WHEN:
On Thursday, November 08, 2001 at 2.30PM

WHERE:
Durham Science Center, Room 255

WHAT:

Dora Matache

UNO

will give a talk on

Operator Self-Similar Processes

Abstract:
Operator Self-Similar (OSS) Processes are a topic at the intersection of the theory of probabilities and functional analysis. The scalar-valued version of this notion is called self-similar processes. Fractional Brownian Motions are probably the most popular class of examples, having various applications. For vector-valued processes, the self-similarity is induced by scaling families of linear operators. This is the reason for the term Operator Self-Similar. This class of processes has been studied so far only in real, finite dimensional, Euclidean spaces. The talk will briefly report on the status of the theory in that framework, and present original results for OSS processes valued in arbitrary Banach spaces. Besides techniques belonging to the theory of stochastic processes and classical functional analysis, the results are based mainly on the theory of one-parameter semigroups of linear operators.