Stochastic reaction networks modeled as jump Markov processes serve as the main mathematical representation of biochemical phenomena in cells, particularly when the relevant molecule count is low, causing deterministic macroscale chemical reaction …
Birth-death processes are discrete-state, continuous-time Markov jump processes with one-step jumps. In this work, first passage times in birth-death processes and their near-continuum (i.e., large system size) limit processes are investigated. Mean …
We investigate the near-continuum asymptotics of mean first passage times in some one-variable birth–death processes. The particular problem we address is how to extract mean first passage times in the near-continuum limit from their defining …
We consider extinction times for a class of birth-death processes commonly found in applications, where there is a control parameter which defines a threshold. Below the threshold, the population quickly becomes extinct; above, it persists for a long …
Diffusion processes intended to model the continuous state space limit of birth–death processes, chemical reactions, and other discrete particle systems often involve multiplicative noise where the diffusion vanishes near one (or more) of the state …