Abstract

In this talk, we introduce a class of time-non-local birth-death processes by applying a time-change, via an independent inverse subordinator, to a class of solvable (classical) birth-death processes. Precisely, we consider a class of birth-death processes with polynomial birth and death rate and whose stationary distribution solves a discrete Pearson equation. In particular, the generator of the parent birth-death processes can be seen as lattice approximations of the generators of the Pearson diffusions. We use a spectral decomposition method to show existence and uniqueness of strong solutions of some time-non-local heat-like Cauchy problems on a sequence space induced by the generator of the birth-death processes and its adjoint operator. The non-local birth-death processes introduced before are then used to exploit a stochastic representation result for such solutions. Finally, some properties of these processes, such as stationarity and long/short-range dependence, are investigated. This talk is based on a joint work with Nikolai Leonenko (Cardiff University) and Enrica Pirozzi (Università  degli Studi di Napoli).