Limiting process of absorbing Markov chains

Abstract

We outline an approach to investigate the limiting law of an absorbing Markov chain conditional on having not been absorbed for long time. The main idea is to employ Donsker-Varadhan’s entropy functional which is typically used as the large deviation rate function for Markov processes. This approach provides an interpretation for a certain quasi-ergodicity

Keywords

Absorbing Markov chain / large deviation / principal eigenvalue / quasi-stationary distribution / decay parameter

References

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Higher Education Press and Springer-Verlag Berlin Heidelberg