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Probabilistic approach and stochastic simulation become more and more popular in all branches of science and technology, especially in problems where the data are randomly fluctuating, or they are highly irregular in deterministic sense. As a rule, in such problems it is very difficult and expensive to carry out measurements to extract the desired data. As important examples the book mentions the turbulent flow simulation in atmosphere, and construction of flows through porous media. The temporal and spatial scales of the input parameters in this class of problems are varying enormously,...

The book presents integral formulations for partial differential equations, with the focus on spherical and plane integral operators. The integral relations are obtained for different elliptic and parabolic equations, and both direct and inverse mean value relations are studied. The derived integral equations are used to construct new numerical methods for solving relevant boundary value problems, both deterministic and stochastic based on probabilistic interpretation of the spherical and plane integral operators.