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

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On decomposition of additive functionals of reflecting Brownian motions,M = (X., P.) on . with the associated Dirichlet form .,. being regular on ..., the following decomposition of additive functionals (AF’s in abbreviaton) is known ([11]): ... — almost surely,which holds for quasi every (q.e. in abbreviation) . ∈ . Here u is a quasi- continuous function in the space F

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Lagrangian for pinned diffusion process,pendent Hilbert spaces ([11], also [10]). Near the end of the 1970s D.Fujiwara succeeded in proving the existence of the limit of finite dimensional path integrals for Schrödinger equations in a very strong sense [3], and later in showing “Itô’s version” [4]. Inspired by their works and looking at t

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Short Time Asymptotics and an Approximation for the Heat Kernel of a Singular Diffusion,t also those associated with the generators with distribution coefficients like measures or even derivatives of measures. That of one-dimensional ones 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 fo

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,Calculus for multiplicative functionals, Itô’s formula and differential equations,’s stochastic analysis has established for itself the central role in modern probability theory. Itô’s theory of stochastic differential equations has been one of the most important tools. However, Itô’s construction of stochastic integrals over Brownian motion possesses an essentially random charac

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