Quasi-Stationary Distributions for Perturbed Discrete Time Regenerative Processes

• 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.

Ämnesord

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Nyckelord

Regenerative process

Renewal equation

Non-linear perturbation

Quasi-stationary distribution

Asymptotic expansion

Risk process

Mathematical Statistics

matematisk statistik

Publikations- och innehållstyp

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