Construction of stochastic processes with singular jump characteristics as solutions of martingale problems

Tuesday, October 23, 2012 - 10:15am - 11:05am
Keller 3-180
Peter Imkeller (Humboldt-Universität)
We construct Lévy processes with discontinuous jump characteristics in
form of weak solutions of appropriate stochastic differential equations, or
related martingale problems with non-local operators. For this purpose we
prove a general existence theorem for martingale problems in which a
sequence of operators generating Feller processes approximates an operator
with a range containing discontinuous functions. The approach crucially
depends on uniform estimates for the probability densities of the
approximating processes derived from properties of the associated symbols.
The theorem is applicable to stable like processes with discontinuous
stability index. This talk is based on work with N. Willrich (WIAS Berlin).
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