For general, almost surely absorbed Markov processes, we obtain necessary and sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process (the process conditioned to never be absorbed). We apply these results to one-dimensional birth and death proce...

In this paper we study the long term evolution of a continuous time Markov chain formed by two interacting birth-and-death processes and motivated by modelling interaction between populations. We show transience/recurrence of the Markov chain under fairly general assumptions on transition rates and describe in more detail its asymptotic behaviour in some transient cases. 1 The model and results...

The spread of an advantageous mutation through a population is fundamental interest in genetics. While the classical Moran model formulated for well-mixed population, it has long been recognized that real-world applications, usually explicit spatial structure which can significantly influence dynamics. In context cancer initiation epithelial tissue, several recent works have analyzed dynamics m...

Integral functionals of Markov processes are widely used in stochastic modeling for applications in ecology, evolution, infectious disease epidemiology, and operations research. The integral of a stochastic process is often called the “cost” or “reward” accrued by the process. Many important stochastic counting models can be written as general birth-death processes (BDPs), which are continuous-...

In the field of Compressed Sensing, estimation sparsity level is very essential as determines minimum number (i) measurements to be obtained a sparse signal during acquisition and (ii) iterations performed for many greedy techniques perfect recovery from measurements. this paper, we propose Maximum Likelihood (ML) estimator estimate instantaneous an ML sequence (MLS) levels recovery. As varies ...