Existence of quasi-stationary distributions for downward skip-free Markov chains.

Abstract: I talk about existence of a quasi-stationary distribution for downward skip-free continuous-time Markov chains on non-negative integers stopped at zero.

The scale function for these processes is introduced and the boundary is classified by a certain integrability condition on the scale function, which gives an extension of Feller’s classification of the boundary for birth-and-death  processes.The existence and the set of quasi-stationary distributions are characterized by the scale function and the new classification of the boundary.

Posted on Mar 6, 2023 in Seminario de Probabilidades de Chile, Seminars