# Paul Krühner: On uniqueness of Markov processes described by a symbol.

Paul Krühner (University of Oslo) holder et seminar med tittelen: On uniqueness of Markov processes described by a symbol.

Abstract:

Stochastic processes used in financial or statistical modelling are usually described by a stochastic differential equation (SDE) or in terms of their Markovian behaviour. The Markovian behaviour can be described in many ways. For instance, one could describe it in terms of an SDE where the solution is Markovian, one could specify the so-called transition semigroup or one can specify a well-posed martingale problem. The first and the latter approach have the advantage that the process specification can be very compact and that it is possible to describe huge classes of processes. Moreover, both of them give an intuitive description of the local behaviour of the process. We use the approach of describing a martingale problem by a symbol and give a result on well-posedness.