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This volume attempts to exhibit current research in stochastic integration, stochastic differential equations, stochastic optimization and stochastic problems in physics and biology. It includes information on the theory of Dirichlet forms, Feynman integration and the Schrodinger's equation.

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Building on the basic techniques of separation of variables and Fourier series, this presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems - rectangular, cylindrical, and spherical.

Random evolution denotes a class of stochastic processes which evolve according to a rule which varies in time according to jumps. This is in contrast to diffusion processes, which assume that the rule changes continuously with time. Random evolutions provide a very flexible language, having the advantage that they permit direct numerical simulation-which is not possible for a diffusion process. Furthermore, they allow connections with hyperbo...

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