# Probability Seminar Essen

## Probability Seminar Essen

Covers a wide range of topics in Probability and its applications.

 Apr 16 Viktor Schulmann, TU Dortmund Apr 23 Sascha Kissel, University Bochum Apr 30 May 7 May 14 May 21 May 28 Jun 4 Jun 18 Jun 25 Jul 2 Jul 9

## Abstracts:

 Apr 16 Viktor Schulmann, TU Dortmund Life span estimation for randomly moving particles based on their places of death Consider the following problem from physics: A radiation source is placed at the center of a screen. At certain time intervals the source releases particles. These move around the screen following a path of some known random process $(Y_t)_{t\geq 0}$ without interacting with each other and without us being able to observe their movement until they die after some random time $T$. During its death a particle leaves a mark such that we can measure the distance $X=||Y_T||_2$ it traveled from the source during its lifetime. Based on these observed distances we wish to infer the life span $T$ of a particle or, in particular, the density $f_T$ of $T$. We assume $(Y_t)_{t\geq 0}$ from our physics experiment to be a multi-dimensional L\'{e}vy processes with spherical symmetry. Norms of such processes exhibit structural similarities to one-dimensional L{\'e}vy processes. For that case an estimator was given by Belomestny and Schoenmakers (2016) using the Mellin and Laplace transforms. Applying their techniques we construct a non-parametrical estimator for $f_T$, calculate its convergence rate and show its optimality in the minimax sense. Apr 23 Sascha Kissel, University Bochum tba.