Quasi-stationary distributions for perturbed discrete time regenerative processes

Petersson, Mikael

doi:10.1090/S0094-9000-2015-00942-X

Quasi-stationary distributions for perturbed discrete time regenerative processes

Author: Mikael Petersson
Journal: Theor. Probability and Math. Statist. 89 (2014), 153-168
MSC (2010): Primary 60K05, 34E10; Secondary 60K25
DOI: https://doi.org/10.1090/S0094-9000-2015-00942-X
Published electronically: January 26, 2015
MathSciNet review: 3235182
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Abstract: Non-linearly perturbed discrete time regenerative processes with regenerative stopping times are considered. We define the quasi-stationary distributions for such processes and present conditions for their convergence. Under some additional assumptions, the quasi-stationary distributions can be expanded in asymptotic power series with respect to the perturbation parameter. We give an explicit recurrence algorithm for calculating the coefficients in these asymptotic expansions. Applications to perturbed alternating regenerative processes with absorption and perturbed risk processes are presented.

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