We consider non-conservative positive semigroups and obtain necessary sufficient conditions for uniform exponential contraction in weighted total variation norm. This ensures the existence of Perron eigenelements provides quantitative estimates spectral gap, complementing Krein–Rutman theorems generalizing probabilistic approaches. The proof is based on a non-homogenous h $h$ -transform semigro...

The notion of N-ple Markov process is defined in a quite general framework and it is shown that N-ple Markov processes-arel inear combinationso f some martingales

introduction preterm birth is still a major health problem throughout the world. preterm birth results in 75% of neonatal mortality. we sought to identify risk factors which cause preterm birth. materials and methods this cross-sectional study assessed all preterm neonates born in asali hospital in khorram abad (either by nvd or c/s) during the first 6 months of 2007. sampling method was census...

The large deviations at Level 2.5 are applied to Markov processes with absorbing states in order obtain the explicit extinction rate of metastable quasi-stationary terms their empirical time-averaged density and flows over a time-window $T$. standard spectral problem for slowest relaxation mode can be recovered from full optimization all these observables equivalence understood via Doob generat...

Background: The term malnutrition generally refers to both under-nutrition and over-nutrition, but this study uses the term to refer solely to a deficiency of nutrition. In Ethiopia, child malnutrition is one of the most serious public health problem and the highest in the world. The purpose of the present study was to identify the high risk factors of malnutrition and test different statistica...

This paper is concerned with the circumstances under which a discrete-time absorbing Markov chain has a quasi-stationary distribution. We showed in a previous paper that a pure birth-death process with an absorbing bottom state has a quasi-stationary distribution – actually an infinite family of quasi-stationary distributions – if and only if absorption is certain and the chain is geometrically...

The cutoff phenomenon describes a case where a Markov chain exhibits a sharp transition in its convergence to stationarity. In 1996, Diaconis surveyed this phenomenon, and asked how one could recognize its occurrence in families of finite ergodic Markov chains. In 2004, the third author noted that a necessary condition for cutoff in a family of reversible chains is that the product of the mixin...

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quant...

Mean-field models are often used to approximate Markov processes with large state-spaces. One-step processes, also known as birth-death processes, are an important class of such processes and are processes with state space {0, 1, . . . , N} and where each transition is of size one. We derive explicit bounds on the expected value of such a process, bracketing it between the mean-field model and ...