Importance Sampling for Pathwise Sensitivity of Stochastic Chaotic Systems

05/25/2020
by   Wei Fang, et al.
0

This paper proposes a new pathwise sensitivity estimator for chaotic SDEs. By introducing a spring term between the original and perturbated SDEs, we derive a new estimator by importance sampling. The variance of the new estimator increases only linearly in time T, compared with the exponential increase of the standard pathwise estimator. We compare our estimator with the Malliavin estimator and extend both of them to the Multilevel Monte Carlo method, which further improves the computational efficiency. Finally, we also consider using this estimator for the SDE with small volatility to approximate the sensitivities of the invariant measure of chaotic ODEs. Furthermore, Richardson-Romberg extrapolation on the volatility parameter gives a more accurate and efficient estimator. Numerical experiments support our analysis.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
11/14/2019

Importance sampling for a robust and efficient multilevel Monte Carlo estimator for stochastic reaction networks

The multilevel Monte Carlo (MLMC) method for continuous time Markov chai...
research
09/27/2022

Using Importance Samping in Estimating Weak Derivative

In this paper we study simulation-based methods for estimating gradients...
research
01/26/2019

Eficient Monte Carlo Simulation of the Left Tail of Positive Gaussian Quadratic Forms

Estimating the left tail of quadratic forms in Gaussian random vectors i...
research
10/02/2017

Oracle Importance Sampling for Stochastic Simulation Models

We consider the problem of estimating an expected outcome from a stochas...
research
05/18/2018

On a Metropolis-Hastings importance sampling estimator

A classical approach for approximating expectations of functions w.r.t. ...
research
01/07/2021

Ensemble approximate control variate estimators: Applications to multi-fidelity importance sampling

The recent growth in multi-fidelity uncertainty quantification has given...
research
01/10/2013

Policy Improvement for POMDPs Using Normalized Importance Sampling

We present a new method for estimating the expected return of a POMDP fr...

Please sign up or login with your details

Forgot password? Click here to reset