Introduction and Outline
The work in the following chapters is given in a research-expository style outlining the current state and containing new perspectives in real and stochastic analysis, essentially with complete details. These articles are prepared by active researchers in the respective areas dealing with problems of current and immediate interest and they are given in an unhurried and detailed manner that will be helpful for senior graduate students engaged in their theses as well as for research mathematicians exploring new problems in the areas covered here. The general point of view is similar to the earlier volumes under the same title; appearing in 1986 and 1997, both edited by me. The subjects covered here complement the earlier volumes and are on stochastic analysis on manifolds (two chapters), noncommutative probability (of interest in quantum mechanics and elsewhere), the non-absolute Feynrnan integration with applications, stochastic flows of diffeomorphisms with some new aspects of Ito (and Stratonovich) calculus, and structural characterizations of locally compact groups based on symmetric random walks on them-arising from algebraic and spectral properties of the associated convolution operators. An outline of each of the chapters will now be given for a bird's-eye view of the overall volume.
KeywordsStochastic Differential Equation Orlicz Space Stochastic Analysis Stochastic Flow Early Volume
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