Titlebook: Itô’s Stochastic Calculus and Probability Theory; Nobuyuki Ikeda (Professor),Shinzo Watanabe (Profes Book 1996 Springer-Verlag Tokyo 1996

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Short Time Asymptotics and an Approximation for the Heat Kernel of a Singular Diffusion, is completely determined in 1950’s and 1960’s by many authors such as W. Feller, K. Itô, H. P. McKean and E.B. Dynkin, among others. The situation for multidimensional ones is however quite different and the problem is still open.

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Some recent developments in nonlinear filtering theory,t the place to describe in detail Professor Itô’s continuing contributions to the subject he helped to create. However, one incident which illustrates his eagerness to explore and assimilate new ideas stands out in my mind.

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Detecting a single defect in a scenery by observing the scenery along a random walk path,serve one of the two sequences {ξ(..)}. or .(..)}., without being told which of the two sequences is observed. If ξ is known, can we decide (with zero probability of error) on the basis of these observations which of the two sequences was observed ? We prove that this can be done for ‘almost all’ ξ, when k≥5.

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Nobuyuki Ikeda (Professor),Shinzo Watanabe (Profes

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experts surveying recent developments. Not only mathematicians but also physicists, biologists, economists and researchers in other fields who are interested in the effectiveness of stochastic theory will find valuable suggestions for their research. In addition, students who are beginning their study and res978-4-431-68534-0978-4-431-68532-6

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