This monograph is devoted to the further development of parametricweight Monte Carlo estimates for solving linear and nonlinearintegral equations, radiation transfer equations, and boundary valueproblems, including problems with random parameters. The use of theseestimates leads to the construction of new, effective Monte Carlomethods for calculating parametric multiple derivatives of solutionsand for the main eigenvalues.
The book opens with an introduction on the theory of weight MonteCarlo methods. The following chapters contain new material on solvingboundary value problems with complex parameters, mixed problems toparabolic equations, boundary value problems of the second and thirdkind, and some improved techniques related to vector and nonlinearHelmholtz equations. Special attention is given to the foundation andoptimization of the global `walk on grid' method for solving theHelmholtz difference equation. Additionally, new Monte Carlo methodsfor solving stochastic radiation transfer problems are presented,including the estimation of probabilistic moments of correspondingcritical parameters.
This monograph will be of value and interest to graduate andpostgraduate researchers in the field of Monte Carlo methods,mathematical physics, radiation transfer theory, and statisticalmodelling, both in academia and industry.
1999; viii+188 pages ISBN 90-6764-297-5 Price (all prices are subject to change without notice): EUR 140/US$ 200
