Simulation of quasi-stationary distributions on countable spaces.

GROISMAN, PABLO; JONCKHEERE, MATTHIEU

MARKOV PROCESSES AND RELATED FIELDS

Polymat

Lugar: Moscu; Año: 2013 vol. 19 p. 521 - 542

1024-2953

Quasi-stationary distributions (QSD) have been widely studied sincethe pioneering work of Kolmogorov (1938), Yaglom (1947) and Sevastyanov (1951).They appear as a natural object when considering Markov processes that are certainly absorbed since they are invariant for the evolution of the distribution of the process conditioned on not being absorbed. They hence appropriately describe the state of the process at largetimes for non absorbed paths. Unlike invariant distributions for Markov processes, QSD are solutions of a non-linear equation and there can be 0, 1 or an infinity of them. Also, they cannot be obtained as Cesaro limits of Markovian dynamics. These facts make the computation of QSDs a nontrivial matter. We review different approximation methods for QSD that are useful for simulation purposes, mainly focused on Fleming-Viot dynamics. We also give some alternative proofs and extensions of known results.