arXiv subjects

Mikael Petersson

Publications and source records attributed to Mikael Petersson.

4 recordsLinked to original sources

arXiv2016

Asymptotic Expansions for Moment Functionals of Perturbed Discrete Time Semi-Markov Processes

In this paper, we study mixed power-exponential moment functionals of nonlinearly perturbed semi-Markov processes in discrete time. Conditions under which the moment functionals of interest can be expanded in asymptotic power series with respect to the perturbation parameter are given. We show how the coefficients in these expansions can be computed from explicit recursive formulas. In particular, the results of the present paper have applications for studies of quasi-stationary distributions.

math.PR↗

arXiv2016

Asymptotics for Quasi-Stationary Distributions of Perturbed Discrete Time Semi-Markov Processes

In this paper, we study quasi-stationary distributions of nonlinearly perturbed semi-Markov processes in discrete time. This type of distributions is of interest for the analysis of stochastic systems which have finite lifetimes, but are expected to persist for a long time. We obtain asymptotic power series expansions for quasi-stationary distributions and it is shown how the coefficients in these expansions can be computed from a recursive algorithm. As an illustration of this algorithm, we present a numerical example for a discrete time Markov chain.

math.PR↗

arXiv2016

Nonlinearly Perturbed Birth-Death-Type Models

Asymptotic expansions for stationary and conditional quasi-stationary distributions of nonlinearly perturbed birth-death-type semi-Markov models are presented. Applications to models of population growth, epidemic spread and population genetics are discussed.

math.PR↗

arXiv2016

Quasi-Stationary Asymptotics for Perturbed Semi-Markov Processes in Discrete Time

We consider a discrete time semi-Markov process where the characteristics defining the process depend on a small perturbation parameter. It is assumed that the state space consists of one finite communicating class of states and, in addition, one absorbing state. Our main object of interest is the asymptotic behaviour of the joint probabilities of the position of the semi-Markov process and the event of non-absorption as time tends to infinity and the perturbation parameter tends to zero. The main result gives exponential expansions of these probabilities together with an recursive algorithm for computing the coefficients in the expansions.

math.PR↗