A micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations

Abstract

We present and analyse a micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations with separation between the (fast) time-scale of individual trajectories and the (slow) time-scale of the macroscopic function of interest. The algorithm combines short bursts of path simulations with extrapolation of a number of macroscopic state variables forward in time. The new microscopic state, consistent with the extrapolated variables, is obtained by a matching operator that minimises the perturbation caused by the extrapolation. We provide a proof of the convergence of this method, in the absence of statistical error, and we analyse various strategies for matching, as an operator on probability measures. Finally, we present numerical experiments that illustrate the effects of the different approximations on the resulting error in macroscopic predictions.

39 pages, 8 figures; added new figure, changes in Sections 6 and 7, corrected typos

References in corpus (7)

• Rooted Tree Analysis for Order Conditions of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential Equations
• Information-theoretic tools for parametrized coarse-graining of non-equilibrium extended systems
• Path-space variational inference for non-equilibrium coarse-grained systems
• Families of efficient second order Runge-Kutta methods for the weak approximation of Itô stochastic differential equations
• Diagonally drift-implicit Runge-Kutta methods of weak order one and two for Itô SDEs and stability analysis
• Stochastic Taylor Expansions for Functionals of Diffusion Processes
• A high-order asymptotic-preserving scheme for kinetic equations using projective integration

Cited by in corpus (4)

• Discovery of slow variables in a class of multiscale stochastic systems via neural networks
• Hierarchical Micro-Macro Acceleration for Moment Models of Kinetic Equations
• Study of micro-macro acceleration schemes for linear slow-fast stochastic differential equations with additive noise
• Convergence of equation-free methods in the case of finite time scale separation with application to deterministic and stochastic systems