There has been a resurgence of interest in non-equilibrium stochastic processes in recent
years, driven in part by the observation that the number of molecules (genes, mRNA …

One of the major challenges in modern biology is to understand how the molecular
components of a living cell operate in a highly noisy environment. What are the specific …

In this paper, we review several results from singularly perturbed differential equations with
multiple small parameters. In addition, we develop a general conceptual framework to …

We give a short overview of recent results on a specific class of Markov process: the
Piecewise Deterministic Markov Processes (PDMPs). We first recall the definition of these …

We construct a path-integral representation of solutions to a stochastic hybrid system,
consisting of one or more continuous variables evolving according to a piecewise …

Computational biology is the science of developing mathematical models and numerical
simulation techniques to understand biological and biochemical systems. Since the early …

The ability to distinguish between stochastic systems based on their trajectories is crucial in
thermodynamics, chemistry, and biophysics. The Kullback–Leibler (KL) divergence, D KL AB …

We obtain large deviation results for a two time-scale model of jump-diffusion processes.
The processes on the two time scales are fully inter-dependent, the slow process has small …

We present a new derivation of the classical action underlying a large deviation principle
(LDP) for a stochastic hybrid system, which couples a piecewise deterministic dynamical …

We consider two approaches to study non-reversible Markov processes, namely the
hypocoercivity theory and general equations for non-equilibrium reversible–irreversible …