Two Types of Time Reversals for Markov Processes

The talk is divided into three parts: In the first part, the classical time reversal for stationary Markov processes is discussed for Piecewise Deterministic Markov Processes (joint work with Zbigniew Palmowski, Wroclaw). As an example we show how one can describe the inverse of the M/G/1-workload process. The remaining two parts are based on work in progress (in the broadest sense). We look at time reversal in the non-stationary case when we specify both a fixed initial distribution and the time T from which the process is to be reversed. With two very simple examples, an innocently looking continuous time Markov chain and the seemingly harmless Poisson process, we demonstrate how time reversal makes sense and leads to interesting results. The last part is concerned with time reversal with fixed distributions at time 0 and at time T and whether this even makes sense.