Time reversal and stationarity of infinite-dimensional Markov birth-and-death processes

Stationarity, Time–reversal and Fluctuation Theory for a Class of Piecewise Deterministic Markov Processes

We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states (x, σ) ∈ Ω × Γ, Ω being a region in R or the d–dimensional torus, Γ being a finite set. The continuous variable x follows a piecewise deterministic dynamics, the discrete variable σ evolves by a stochastic jump dynamics and the two resulting evolutions are fully–coupled. We study st...

Spatial Birth-and-Death Markov Processes

ON THE INFINITE ORDER MARKOV PROCESSES

The notion of infinite order Markov process is introduced and the Markov property of the flow of information is established.

On the Convergence to Stationarity of Birth-death Processes

Taking up a recent proposal by Stadje and Parthasarathy in the setting of the many-server Poisson queue, we consider the integral ∫∞ 0 [limu→∞E(X(u))− E(X(t))]dt as a measure of the speed of convergence towards stationarity of the process {X(t), t ≥ 0}, and evaluate the integral explicitly in terms of the parameters of the process in the case that {X(t), t ≥ 0} is an ergodic birth-death process...

Smoothness of Harmonic Functions and Time Reversal of Markov Processes

A new probabilistic proof is given for the C 1 smoothness of solutions of PDEs Lh = `, when L is a second order diierential operator satisfying the HH ormander condition; this proof is based on a time reversal result. Then the technique is extended to non local operators L associated to Markov processes with jumps, and the smoothness of solutions of Lh = ` is again studied. R egularit e des fon...