Titlebook: Bernoulli 1713, Bayes 1763, Laplace 1813; Anniversary Volume. Jerzy Neyman,Lucien M. Cam Conference proceedings 1965 Springer-Verlag Berli

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Stationary and Isotropic Random Functions,We are going to deal with random functions . (.) = . (.., ... , ..) of a point . (..: .-dimensional Euclidean space). We assume:

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First-Passage Percolation, Subadditive Processes, Stochastic Networks, and Generalized Renewal Theo.. In 1957, Broadbent and Hammersley gave a mathematical formulation of percolation theory. Since then much work has been done in this field and has now led to first-passage percolation problems. In the following two examples we contrast the early formulation with its more recent developments.

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Strong Limit Theorems for Stochastic Processes and Orthogonality Conditions for Probability MeasureLet . (.), 0≦.≦., be the Wiener process, that is, a real Gaussian stochastic process with . and let .. for . = 1, 2,... be the sequence of increasing integers. Consider the following functional of . (.): . In 1940 . [.] discovered the following interesting result concerning this functional.

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