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Nonlinear dynamics is now recognized as playing a crucial role in a
wide variety of disciplines. But what is only just beginning is the
important process of cross fertilization and transfer of knowledge
and expertise from one area to another. This book is intended to
promote this process which will undoubtedly contribute greatly to
furthering our understanding of complex systems. Contributions are
provided by leading experts from the areas of sociology, cognitive
science, chemistry, physiology, ecology, economics, neural networks
and physics.
The Monte Carlo method is based on the munerical realization of
natural or artificial models of the phenomena under considerations.
In contrast to classical computing methods the Monte Carlo
efficiency depends weakly on the dimen sion and geometric details
of the problem. The method is used for solving complex problems of
the radiation transfer theory, turbulent diffusion, chemi cal
kinetics, theory of rarefied gases, diffraction of waves on random
surfaces, etc. The Monte Carlo method is especially effective when
using multi-processor computing systems which allow many
independent statistical experiments to be simulated simultaneously.
The weighted Monte Carlo estimates are constructed in order to
diminish errors and to obtain dependent estimates for the
calculated functionals for different values of parameters of the
problem, i.e., to improve the functional dependence. In addition,
the weighted estimates make it possible to evaluate special
functionals, for example, the derivatives with respect to the
parameters. There are many works concerned with the development of
the weighted estimates. In Chap. 1 we give the necessary
information about these works and present a set of illustrations.
The rest of the book is devoted to the solution of a series of
mathematical problems related to the optimization of the weighted
Monte Carlo estimates."
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