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Quasi-stationary distributions for perturbed discrete time regenerative processes


Author: Mikael Petersson
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 89 (2013).
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
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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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Additional Information

Mikael Petersson
Affiliation: Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden
Email: mikpe@math.su.se

DOI: https://doi.org/10.1090/S0094-9000-2015-00942-X
Keywords: Regenerative process, renewal equation, non-linear perturbation, quasi-stationary distribution, asymptotic expansion, risk process
Received by editor(s): November 11, 2012
Published electronically: January 26, 2015
Article copyright: © Copyright 2015 American Mathematical Society