General criteria for the study of quasi-stationarity

By Nicolas Champagnat, Denis Villemonais. Electronic Journal of Probability, 2017

94 citations recorded by the source corpus.

For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential non-uniform convergence in total variation norm to a quasi-stationary distribution. We also characterize a subset of its domain of attraction by an integrability condition, prove the existence of a right eigenvector for the semigroup of the process and the existence and exponential ergodicity of the Q-process. These results are applied to one-dimensional and multi-dimensional diffusion processes, to pure jump continuous time processes, to reducible processes with several communication classes, to perturbed dynamical systems and discrete time processes evolving in discrete state spaces.

Subfields: Finance, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4e279613b1395af3b2b105dea968531549948c23

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In Finance

1. Vincent Bansaye
2. Pierre Gabriel
3. Aline Marguet
4. Bertrand Cloez
5. Jinghai Shao

In Mathematical Physics

1. Bertrand Cloez
2. Vincent Bansaye
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In Statistics and Probability

1. Vincent Bansaye
2. Pierre Gabriel
3. Bertrand Cloez
4. Aline Marguet
5. Jinghai Shao

Citations in the corpus

• A non‐conservative Harris ergodic theorem (2019, methodology): “Assumption A is linked and relax classical assumptions for the ergodicity of non-conservative semigroups [1, 9, 26, 48, 61, 63, 64, 77, 90, 91, 93].”