Ratio Limits and Limiting Conditional Distributions for Discrete-Time Birth-Death Processes

Limiting Conditional Distributions for Birth-death Processes

In a recent paper [16], one of us identified all of the quasi-stationary distributions for a non-explosive, evanescent birth-death process for which absorption is certain, and established conditions for the existence of the corresponding limiting conditional distributions. Our purpose is to extend these results in a number of directions. We shall consider separately two cases depending on wheth...

Families of ν-similar birth-death processes and limiting conditional distributions

*Correspondence: [email protected] Faculty of Computer Science, Bialystok University of Technology, ul. Wiejska 45A, Białystok, 15-351, Poland Abstract We study, for a given process X , the conditions under which ν-similarity is provided, relations between similarity and ν-similarity of processes, and we analyze (doubly) limiting conditional distributions. We present sufficient conditions f...

Limiting Distributions for Critical Multitype Branching Processes with Discrete Time(')

Discrete evolutionary birth-death processes and their large population limits

We study a class of discrete-state Markovian models of evolutionary population dynamics for k types of organisms, called discrete evolutionary birth-death processes (EBDP). The organisms in a model environment interact with each other by playing a certain game. Birth rates for type i organisms at time t are determined by their expected payoff in the game against an opponent chosen randomly from...

Conditional Processes Induced by Birth and Death Processes

For birth and death processes with finite state space, we consider stochastic processes induced by conditioning on hitting the right boundary point before hitting the left boundary point. We call the induced stochastic processes the conditional processes. We show that the conditional processes are again birth and death processes when the right boundary point is absorbing. On the other hand, it ...