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 …

Rule‐based modeling was developed to address the limitations of traditional approaches for
modeling chemical kinetics in cell signaling systems. These systems consist of multiple …

Monte Carlo methods are a very general and useful approach for the estimation of
expectations arising from stochastic simulation. However, they can be computationally …

This book, as with others in the series, is intended to provide supplementary material for
courses in probability or stochastic processes. The mathematical focus is on counting …

For a function g (h), we write g (h)= O (hp) to mean that there exist constants h0> 0 and K> 0
(independent of h) such that| g (h)|< Khp for all| h|< h0. In words, this means that g (h) tends …

Stochasticity is a key characteristic of intracellular processes such as gene regulation and
chemical signalling. Therefore, characterizing stochastic effects in biochemical systems is …

Stochastic models of biomolecular reaction networks are commonly employed in systems
and synthetic biology to study the effects of stochastic fluctuations emanating from reactions …

We present an efficient finite difference method for the computation of parameter sensitivities
that is applicable to a wide class of continuous time Markov chain models. The estimator for …

This is a textbook for advanced undergraduate students and beginning graduate students in
applied mathematics. It presents the basic mathematical foundations of stochastic analysis …

The dynamics of molecular systems is an essential tool of systems biology. It helps figuring
out what is the effect of the perturbation of a system, or what is the best dose for a drug or …