Variance reduction for Monte Carlo simulation of stochastic environmental models

摘要

To determine the probability of exceedence Monte Carlo simulation of stochastic models is often used. Mathematically this requires the evaluation of an expectation of some function of a solution of a stochastic Model. This can be reformulated as a Kolmogorov final value problem. It can thus be calculated numer- Ically by either solving a deterministic partial differential equation (Kolmogorov's Backwards equations) or By simulating large number of trajectories of the stochastic differential equation.