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Titlebook: Introduction to Infinite Dimensional Stochastic Analysis; Zhi-yuan Huang,Jia-an Yan Book 2000 Springer Science+Business Media Dordrecht 20

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书目名称Introduction to Infinite Dimensional Stochastic Analysis
编辑Zhi-yuan Huang,Jia-an Yan
视频videohttp://file.papertrans.cn/474/473773/473773.mp4
丛书名称Mathematics and Its Applications
图书封面Titlebook: Introduction to Infinite Dimensional Stochastic Analysis;  Zhi-yuan Huang,Jia-an Yan Book 2000 Springer Science+Business Media Dordrecht 20
描述The infinite dimensional analysis as a branch of mathematical sciences was formed in the late 19th and early 20th centuries. Motivated by problems in mathematical physics, the first steps in this field were taken by V. Volterra, R. GateallX, P. Levy and M. Frechet, among others (see the preface to Levy[2]). Nevertheless, the most fruitful direction in this field is the infinite dimensional integration theory initiated by N. Wiener and A. N. Kolmogorov which is closely related to the developments of the theory of stochastic processes. It was Wiener who constructed for the first time in 1923 a probability measure on the space of all continuous functions (i. e. the Wiener measure) which provided an ideal math­ ematical model for Brownian motion. Then some important properties of Wiener integrals, especially the quasi-invariance of Gaussian measures, were discovered by R. Cameron and W. Martin[l, 2, 3]. In 1931, Kolmogorov[l] deduced a second partial differential equation for transition probabilities of Markov processes order with continuous trajectories (i. e. diffusion processes) and thus revealed the deep connection between theories of differential equations and stochastic processes
出版日期Book 2000
关键词Operator theory; Probability theory; Stochastic calculus; Variation; abstract harmonic analysis; distribu
版次1
doihttps://doi.org/10.1007/978-94-011-4108-6
isbn_softcover978-94-010-5798-1
isbn_ebook978-94-011-4108-6
copyrightSpringer Science+Business Media Dordrecht 2000
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Stochastic Calculus of Variation for Wiener Functionals,especially to the probabilistic proof of Hörmander’s theorem on hypoellipticity of partial differential operators. Moreover, we introduce two important branches in this area which were developed very recently: the quasi sure analysis and the anticipating stochastic calculus.
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Book 2000in[l, 2, 3]. In 1931, Kolmogorov[l] deduced a second partial differential equation for transition probabilities of Markov processes order with continuous trajectories (i. e. diffusion processes) and thus revealed the deep connection between theories of differential equations and stochastic processes
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nd W. Martin[l, 2, 3]. In 1931, Kolmogorov[l] deduced a second partial differential equation for transition probabilities of Markov processes order with continuous trajectories (i. e. diffusion processes) and thus revealed the deep connection between theories of differential equations and stochastic processes978-94-010-5798-1978-94-011-4108-6
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Introduction to Infinite Dimensional Stochastic Analysis
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