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Exponential functionals of LÃ©vy processes appear as stationary distributions of generalized Ornstein-Uhlenbeck (GOU) processes. In this paper we obtain the infinitesimal generator of the GOU processâ€¦ (More)

- Anita Behme
- 2011

The generalized Ornstein-Uhlenbeck process Vt = e âˆ’Î¾t ( V0 + âˆ« t 0 edÎ·s ) , t â‰¥ 0, driven by a bivariate LÃ©vy process (Î¾t, Î·t)tâ‰¥0 with starting random variable V0 independent of (Î¾, Î·) fulfills theâ€¦ (More)

De Haan and Karandikar [12] introduced generalized Ornsteinâ€“Uhlenbeck processes as one-dimensional processes (Vt)tâ‰¥0 which are basically characterized by the fact that for each h > 0 theâ€¦ (More)

For a given bivariate LÃ©vy process (Ut, Lt)tâ‰¥0, necessary and sufficient conditions for the existence of a strictly stationary solution of the stochastic differential equation dVt = Vtâˆ’ dUt + dLt areâ€¦ (More)

- Anita Behme, Claudia KlÃ¼ppelberg, Kathrin Mayr
- J. Applied Probability
- 2014

- Anita Behme, Alexander Schnurr
- 2013

An integral criterion for the existence of an invariant measure of an ItÃ´ process is developed. This new criterion is based on the probabilistic symbol of the ItÃ´ process. In contrast to the standardâ€¦ (More)

We characterize the support of the law of the exponential functional âˆ«âˆž 0 e âˆ’Î¾sâˆ’ dÎ·s of two independent LÃ©vy processes Î¾ and Î·. Further, we study the range of the mapping Î¦Î¾ for a fixed LÃ©vy processâ€¦ (More)

- Anita Behme
- J. Multivariate Analysis
- 2012

Moment conditions for multivariate generalized Ornstein-Uhlenbeck (MGOU) processes are derived and first and second moment are given in terms of the driving LÃ©vy processes. In the second part of theâ€¦ (More)

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