Importance Sampling for Multiscale Diffusions

Abstract

We construct importance sampling schemes for stochastic differential equations with small noise and fast oscillating coefficients. Standard Monte Carlo methods perform poorly for these problems in the small noise limit. With multiscale processes there are additional complications, and indeed the straightforward adaptation of methods for standard small noise diffusions will not produce efficient schemes. Using the subsolution approach we construct schemes and identify conditions under which the schemes will be asymptotically optimal. Examples and simulation results are provided.

Cited by in corpus (19)

• Large Deviations for Multiscale Diffusions via Weak Convergence Methods
• Bistable switching asymptotics for the self regulating gene
• Large Deviations and Importance Sampling for Systems of Slow-Fast Motion
• Large and moderate deviations for stochastic Volterra systems
• Escaping from an attractor: Importance sampling and rest points I
• Importance sampling in path space for diffusion processes with slow-fast variables
• A Koopman framework for rare event simulation in stochastic differential equations
• Dynamical systems with fast switching and slow diffusion: Hyperbolic equilibria and stable limit cycles
• On a new class of score functions to estimate tail probabilities of some stochastic processes with Adaptive Multilevel Splitting
• Jarzynski's equality, fluctuation theorems, and variance reduction: Mathematical analysis and numerical algorithms
• Nonasymptotic bounds for suboptimal importance sampling
• Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics
• A large deviation principle for Markovian slow-fast systems
• Learning-Based Importance Sampling via Stochastic Optimal Control for Stochastic Reaction Networks
• Importance sampling for thermally induced switching and non-switching probabilities in spin-torque magnetic nanodevices
• Large Deviations of Irreversible Processes
• Importance sampling for slow-fast diffusions based on moderate deviations
• Symmetrized importance samplers for stochastic differential equations
• Estimating Small Probabilities for Langevin Dynamics