On the existence and the applications of modified equations for stochastic differential equations by Zygalakis, K

“… In this paper we describe a general framework for deriving modified equations for stochastic differential equations (SDEs) with respect to weak convergence. …”

Second weak order explicit stabilized methods for stiff stochastic differential equations by Abdulle, A, Vilmart, G, Zygalakis, K

“…We introduce a new family of explicit integrators for stiff Itˆo stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of onestep stabilized methods with extended stability domains and do not suffer from stepsize reduction that standard explicit methods face. …”

High order weak methods for stochastic differential equations based on modified equations by Abdulle, A, Cohen, D, Vilmart, G, Zygalakis, K

“…Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrated with the constructions of new high order weak methods, in particular, implicit integrators well suited for stiff stochastic problems, and integrators that exactly conserve all quadratic first integrals of a stochastic dynamical system. …”

Multi-level Monte Carlo methods for the approximation of invariant measures of stochastic differential equations by Giles, M, Majka, M, Szpruch, L, Vollmer, S, Zygalakis, K

A Constrained Approach to Multiscale Stochastic Simulation of Chemically Reacting Systems by Cotter, S, Zygalakis, K, Kevrekidis, I, Erban, R

“…We then show how using the ensuing Stochastic Differential Equation (SDE) approximation, we can in turn approximate average switching times in stochastic chemical systems.…”

Fast stochastic simulation of biochemical reaction systems by alternative formulations of the Chemical Langevin Equation by Mélykúti, B, Burrage, K, Zygalakis, K

“…The Chemical Langevin Equation (CLE), which is a stochastic differential equation (SDE) driven by a multidimensional Wiener process, acts as a bridge between the discrete Stochastic Simulation Algorithm and the deterministic reaction rate equation when simulating (bio)chemical kinetics. …”

Higher-order numerical methods for stochastic simulation of chemical reaction systems by Székely Jr., T, Burrage, K, Erban, R, Zygalakis, K

“…This approach, as in the case of ordinary and stochastic differential equations, can be repeated to obtain even higher-order approximations. …”

A higher-order numerical framework for stochastic simulation of chemical reaction systems. by Székely, T, Burrage, K, Erban, R, Zygalakis, K

“…As in the case of ordinary and stochastic differential equations, extrapolation can be repeated to obtain even higher-order approximations. …”

A higher-order numerical framework for stochastic simulation of chemical reaction systems by Szekely, T, Burrage, K, Erban, R, Zygalakis, K

“…As in the case of ordinary and stochastic differential equations, extrapolation can be repeated to obtain even higher-order approximations.…”