Anita Behme

A Criterion for Invariant Measures of Ito Processes based on the Symbol

An integral criterion for the existence of an invariant measure of an Ito process is developed. This new criterion is based on the probabilistic symbol of the Ito process. In contrast to the standard integral criterion for invariant measures of Markov processes based on the generator, no test functions and hence no information on the domain of the generator is needed.

Distributions of exponential integrals of independent increment processes related to generalized gamma convolutions

It is known that in many cases distributions of exponential integrals of Levy processes are infinitely divisible and in some cases they are also selfdecomposable. In this paper, we give some sufficient conditions under which distributions of exponential integrals are not only selfdecomposable but furthermore are generalized gamma convolution. We also study exponential integrals of more general independent increment processes. Several examples are given for illustration.

Moments of MGOU processes and positive semidefinite matrix processes

Moment conditions for multivariate generalized Ornstein-Uhlenbeck (MGOU) processes are derived and the first and second moments are given in terms of the driving Levy processes. In the second part of the paper a class of multivariate, positive semidefinite processes of MGOU-type is developed and suggested for use as squared volatility process in multivariate financial modeling.