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Titlebook: Classical Potential Theory and Its Probabilistic Counterpart; Advanced Problems J. L. Doob Book 1984 Springer-Verlag New York Inc. 1984 Mar

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書(shū)目名稱(chēng)Classical Potential Theory and Its Probabilistic Counterpart
副標(biāo)題Advanced Problems
編輯J. L. Doob
視頻videohttp://file.papertrans.cn/228/227123/227123.mp4
叢書(shū)名稱(chēng)Grundlehren der mathematischen Wissenschaften
圖書(shū)封面Titlebook: Classical Potential Theory and Its Probabilistic Counterpart; Advanced Problems J. L. Doob Book 1984 Springer-Verlag New York Inc. 1984 Mar
描述Potential theory and certain aspects of probability theory are intimately related, perhaps most obviously in that the transition function determining a Markov process can be used to define the Green function of a potential theory. Thus it is possible to define and develop many potential theoretic concepts probabilistically, a procedure potential theorists observe withjaun- diced eyes in view of the fact that now as in the past their subject provides the motivation for much of Markov process theory. However that may be it is clear that certain concepts in potential theory correspond closely to concepts in probability theory, specifically to concepts in martingale theory. For example, superharmonic functions correspond to supermartingales. More specifically: the Fatou type boundary limit theorems in potential theory correspond to supermartingale convergence theorems; the limit properties of monotone sequences of superharmonic functions correspond surprisingly closely to limit properties of monotone sequences of super- martingales; certain positive superharmonic functions [supermartingales] are called "potentials," have associated measures in their respective theories and are subject
出版日期Book 1984
關(guān)鍵詞Markov process; Martingale; Motion; Potential theory; Probability theory; Transition function
版次1
doihttps://doi.org/10.1007/978-1-4612-5208-5
isbn_ebook978-1-4612-5208-5Series ISSN 0072-7830 Series E-ISSN 2196-9701
issn_series 0072-7830
copyrightSpringer-Verlag New York Inc. 1984
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The Fine Topologyn . is said to be . than .) if . ? .. For any family of extended real-valued functions on a space there is a coarsest topology making every member of the family continuous, namely, the intersection of all the topologies doing this. The . topology of classical potential theory is defined as the coars
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Classical Energy and Capacityductor, if . is a connected conducting body in ?., the charge on A distributes itself in such a way that the net effect is that of an all-positive or all-negative charge, and the distribution on . is in equilibrium in the sense that the restriction to . of the potential of the charge distribution in
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Parabolic Potential Theory: Basic Factst operator . and its adjoint ., called ., will be developed in Chapters XV to XIX. Concepts that are parabolic counterparts of classical concepts will be distinguished by dots or asterisks, depending on whether the concepts are related to . or to .. Just as the domains of classical potential theory
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The Parabolic Dirichlet Problem, Sweeping, and Exceptional Setsabolic if . is parabolic, superparabolic, or sub-parabolic, respectively. The notation will be parallel to that in the classical context, with . omitted when .. Thus .,... need no further identification. In the dual context in which . is coparabolic we write
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Classical Potential Theory and Its Probabilistic Counterpart978-1-4612-5208-5Series ISSN 0072-7830 Series E-ISSN 2196-9701
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