Abstract:
In this talk, we analyze three different perspectives on the so called probabilistic symbol. Furthermore, we show how the symbol and the related
indices can be used in order to analyze the corresponding stochastic process. The applications under consideration include growth conditions, Hölder conditions, killing, simulations of the process and the strong variation.
In the second part of the talk we focus on one particular application: we derive a criterion for invariant measures which is based on the symbol.
Bibliography:
[1] Behme, A. and Schnurr, A. (2014+): A Criterion for Invariant Measures
of Ito Processes Based on the Symbol. submitted.
[2] Schnurr, A. (2013): Generalization of the Blumenthal-Getoor Index to
the Class of Homogeneous Diffusions with Jumps and Some Applications.
Bernoulli 19(5A) (2013), 2010-2032.