We present a simple and general framework to simulate statistically correct realizations of a
system of non-Markovian discrete stochastic processes. We give the exact analytical …

We study a stochastic model of protein dynamics that explicitly includes delay in the
degradation. We rigorously derive the master equation for the processes and solve it exactly …

Single-cell RNA sequencing data can be modeled using Markov chains to yield genome-
wide insights into transcriptional physics. However, quantitative inference with such data …

The serial nature of reactions involved in the RNA life-cycle motivates the incorporation of
delays in models of transcriptional dynamics. The models couple a transcriptional process to …

In this paper, the stationary probability distribution (SPD) and mean first passage time
(MFPT) in a vegetation model with time delay are investigated, where the vegetation …

Delays are ubiquitous, pervasive, and entrenched in everyday life, thus taking it into
consideration is necessary. Dupire recently developed a functional Itô formula, which has …

The stochastic simulation algorithm (SSA) describes the time evolution of a discrete
nonlinear Markov process. This stochastic process has a probability density function that is …

Stochasticity in gene expression gives rise to fluctuations in protein levels across a
population of genetically identical cells. Such fluctuations can lead to phenotypic variation in …

The serial nature of reactions involved in the RNA life-cycle motivates the incorporation of
delays in models of transcriptional dynamics. The models couple a bursty or switching …

We discuss two models of interpersonal interactions with delay. The first model is linear, and
allows the presentation of a rigorous mathematical analysis of stability, while the second is …