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03967776 Ermakov, S.M. Mikhajlov, G.A. Statistical simulation. Textbook. (Statisticheskoe modelirovanie. Uchebnoe posobie). 2nd ed., suppl. Ministerstvo Vysshego i Srednego Spetsial'nogo Obrazovaniya SSSR. Moskva: "Nauka" Glavnaya Redaktsiya Fiziko-Matematicheskoj Literatury. 296 p. (1982). 1982 RU Monte Carlo method exponential distribution multivariate isotropic vector stochastic processes multivariate Gauss-Markov process stationary process with a known spectral density quadrature formulas variance reduction techniques integral equations walk on a sphere Dirichlet problem nonlinear equations Boltzmann equation branching processes queueing systems partial differential equations exercises This is a second edition of a textbook first published in 1976. The book contains a systematic development of the Monte Carlo method and its applications and consists of six chapters. The first chapter presents methods for computer generation of uniform and nonuniform random variables and random vectors. Here, some interesting methods discussed are related to generation of an exponential distribution and to a multivariate isotropic vector. The second chapter presents some methods for computer generation of stochastic processes and the general framework of the Monte Carlo method. Some interesting results related to generation of a multivariate Gauss-Markov process and to generation of a stationary process with a known spectral density are presented. Methods for generating random fields are also given. As concerns the Monte Carlo method, statistical estimation theory and the use of limit theorems are also discussed. Chapter three is devoted to Monte Carlo methods for calculating various types of integrals. Special attention is paid to stochastic quadrature formulas and to variance reduction techniques. The fourth chapter deals with Monte Carlo methods for solving integral equations and their application to radiation transfer. Apart from the known Monte Carlo techniques, a section of this chapter describes particular problems of calculation of a nuclear reactor. Chapter five develops applications of Monte Carlo methods to solve various problems of numerical analysis and mathematical physics such as: "walk on a sphere" and solving the Dirichlet problem related to this walk; solving nonlinear equations; the Boltzmann equation; branching processes and nonlinear equations. The last chapter (the sixth) presents some theoretical problems of simulating queueing systems with particular reference to methods of increasing the efficiency of simulation models for these systems. The new problems developed in this second edition of the book are mainly related to methods of solving partial differential equations, of solving practical problems of radiation transfer, and to methods of computer generation of stochastic processes. Chapters related to nonlinear problems are also revised. Each chapter contains a set of problems and exercises mainly addressed to students specializing in applied mathematics. Nevertheless, taking into account the deep mathematical treatment of problems presented in this book, it is useful for all research workers in the field of Monte Carlo methods.