Variance reduction for Monte Carlo simulation of stochastic environmental models
The authors consider stochastic differential equations which arise in problems of environmental modelling via the interpretation of the advection-diffusion equation as a Fokker-Planck equation. By using Monte Carlo simulations they intend to determine the probability of the event that some biochemical substances reach a critical region or exceed a critical value. Mathematically this requires the evaluation of the expectation of some function of the solution of the stochastic differential equation. They discuss the numerical efficiency of Monte-Carlo simulations and propose a variance reduction technique to enhance the efficiency. The variance reduction is obtained by the Girsanov transformation to modify the stochastic model by a correction term that is obtained from an approximate solution of the partial differential equation given by the backward Kolmogorov problem and computed by a classical numerical method. They provide numerical examples of the approach showing the enhanced efficiency of it. Finally, the approach is applied to estimate the probability of exceedence in a model for biochemical-oxygen demand.
scientific article; zbMATH DE number 1878790