Optimization of Weighted Monte Carlo Methods Book

Weighted Monte Carlo algorithms are extremely useful when direct simulation techniques are inapplicable or ineffective. The methods presented in this book help to minimize computer time and memory required in constructing statistical models for systems described by integral equations. Approximate solutions of integral and differential equations serve as weighted functionals of special Markov chains. Variances of these solutions are minimized by (nonlinear) "importance" functions for the determination of which the author presents an asymptotic approach. Key points: Optimization of randomized algorithms for estimating probabilistic characteristics of equations with random parameters and applications; computational models for random fields and numerical simulations; vector Monte Carlo algorithms for solving systems of integral equations; a special approach to the application of perturbation theory based on this method.