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Title
Sobolev spaces of generalised smoothness and sub-Markovian semigroups

Abstract
It is cornerstone in the thory of modern theory of stochastic processes that to each (regular) Dirichlet form one can associate a stochastic process. From the probabilistic point of view there is a disadvantage to work with processes associated with Dirichlet spaces because the process is defined only up to an exceptional set (sets of capacity zero). We propose an L_P setting to overcome this difficulty and introduce and (investigate) certain Bessel potential spaces associated with a sub-Markovian semigroup. We show that these spaces are domains of definitions for pseudo-differential operators associated to a continuous negative definite function and some of them can be regarded as Triebel-Lizorkin spaces of generalized smoothness. This allows us in particular to indicate and characterize a large class of Markov processes starting in every point of the euclidean space. Parts of this talk are selected from some recent joint works with N. Jacob, H.-G.Leopold and R. Schilling.

Speaker(s)
Erich Walter Farkas (Swiss Banking Institute/University of Zurich)

Date
May 14, 2004

Time
14.30

Room
Room 5.5

 
     
 

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