Importance Sampling for Pathwise Sensitivity of Stochastic Chaotic Systems

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