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内容説明 This work is devoted to high-dimensional (or large-scale) diffusion stochastic processes (DSPs) with nonlinear coefficients. These processes are closely associated with nonlinear Ito’s stochastic ordinary differential equations (ISODEs) and with the space-discretized versions of nonlinear Ito’s stochastic partial integro-differential equations. The latter models include Ito’s stochastic partial differential equations (ISPDEs). The book presents the new analytical treatment which can serve as the basis of a combined， analytical-numerical approach to the greater computational efficiency in engineering problems. A few examples discussed in the book include: the high-dimensional DSPs; the modification of the well-known stochastic-adaptive-interpolation method by means of bases of function spaces; ISPDEs as the tool to consistently model non-Markov phenomena; the ISPDE system for semiconductor devices; the corresponding classification of charge transport in macroscale， mesoscale and microscale semiconductor regions based on the wave-diffusion equation; the fully time-domain nonlinear-friction aware analytical model for the velocity covariance of particle of uniform fluid， simple or dispersed; the specific time-domain analytics for the long， non-exponential ?tails? of the velocity in case of the hard-sphere fluid. These examples demonstrate not only the capabilities of the developed techniques but also emphasize the usefulness of the complex-system-related approaches to solve some problems which have not been solved with the traditional， statistical-physics methods yet. From this viewpoint， the book can be regarded as a kind of complement to such books as ?Introduction to the Physics of Complex Systems: the Mesoscopic Approach to Fluctuations， Nonlinearity and Self-Organization? by Serra， Andretta， Compiani and Zanarini， ?Stochastic Dynamical Systems: Concepts， Numerical Methods， Data Analysis? and ?Statistical Physics: An Advanced Approach with Applications? by Honerkamp， which deal with physics of complex systems， some of the corresponding analysis methods and an innvoative， stochastics-based vision of theoretical physics. To facilitate the reading by non-mathematicians， the introductory chapter outlines the basic notions and results of theory of Markov and diffusion stochastic processes without involving the measure-theoretical approach. This presentation is based on probability densities commonly used in engineering and applied sciences.