Absolute continuity of the invariant measure in Piecewise Deterministic Markov Processes having degenerate jumps

2016/01/26 by Löcherbach, Eva · 1 citation
#60G55 (Secondary) #60Hxx (Primary) #60J75 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1601.07123

Abstract

We consider piecewise deterministic Markov processes with degenerate transition kernels of the "house-of-cards"-type. We use a splitting scheme based on jump times to prove the absolute continuity, as well as some regularity, of the invariant measure of the process. Finally, we obtain finer results on the regularity of the one-dimensional marginals of the invariant measure, using integration by parts with respect to the jump times.

Cited by

• Analysis of a mean-field limit of interacting two-dimensional nonlinear integrate-and-fire neurons

Related

• Qualitative properties of certain piecewise deterministic Markov processes
• Piecewise Deterministic Markov Processes and their invariant measures
• A note on the jump locations of Markov processes
• A new characterization of the jump rate for piecewise-deterministic Markov processes with discrete transitions
• On Time Reversal of Piecewise Deterministic Markov Processes