Multiscale integrators for stochastic differential equations and irreversible Langevin samplers
Abstract
We study multiscale integrator numerical schemes for a class of stiff stochastic differential
equations (SDEs). We consider multiscale SDEs that behave as diffusions on graphs
as the stiffness parameter goes to its limit. Classical numerical discretization schemes,
such as the Euler-Maruyama scheme, become unstable as the stiffness parameter converges
to its limit and appropriate multiscale integrators can correct for this. We rigorously
establish the convergence of the numerical method to the related diffusion on graph,
identifying the appropriate choice of discretization parameters. Theoretical results
are supplemented by numerical studies on the problem of the recently developing area
of introducing irreversibility in Langevin samplers in order to accelerate convergence
to equilibrium.
Type
Journal articlePermalink
https://hdl.handle.net/10161/14054Collections
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Show full item recordScholars@Duke
Jianfeng Lu
Professor of Mathematics
Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm
development for problems from computational physics, theoretical chemistry, materials
science and other related fields.More specifically, his current research focuses include:Electronic
structure and many body problems; quantum molecular dynamics; multiscale modeling
and analysis; rare events and sampling techniques.

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