Variance reduction for Monte Carlo simulation of stochastic environmental models
type: Item
instance of: scholarly article
title: Variance reduction for Monte Carlo simulation of stochastic environmental models
zbMATH Open document ID: 1014.92046
DOI: 10.1016/S0307-904X(01)00091-9
author: K. Ponnambalam
author: Peter E. Kloeden
author: John Schoenmakers
author: A. W. Heemink
published in: Applied Mathematical Modelling
publication date: 2003-03-10T00:00:00Z
review text: 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.
reviewed by: Evelyn Buckwar
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 65C50
zbMATH DE Number: 1878790
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: environmental modelling
zbMATH Keywords: weak approximations
zbMATH Keywords: variance reduction
zbMATH Keywords: Monte-Carlo method
zbMATH Keywords: Girsanov transformation
MaRDI profile type: Publication
cites work: Higher-order implicit strong numerical schemes for stochastic differential equations
cites work: A survey of numerical methods for stochastic differential equations
cites work: Q3707286
cites work: Q3993078
full work available at URL: s0307-904x(01)00091-9
OpenAlex ID: W2014221443
description: scientific article; zbMATH DE number 1878790