Titlebook: Seminar on Stochastic Processes, 1990; E. Çinlar,P. J. Fitzsimmons,R. J. Williams Book 1991 Springer Science+Business Media New York 1991

安装

,Paul Lévy’s Way to His Local Time,In his 1939 paper [1] Lévy introduced the notion of local time for Brownian motion. He gave several equivalent definitions, and towards the end of that long paper he proved the following result. Let ∈ > 0, . > 0, .(0) = 0,. where .(.) is the Brownian motion in . and . is the Lebesgue measure. Then almost surely the limit below exists for all . >0:

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Seminar on Stochastic Processes, 1990978-1-4684-0562-0Series ISSN 1050-6977 Series E-ISSN 2297-0428

轻浮思想

Transformations of Measure on an Infinite Dimensional Vector Space,.(B) = .(T.(B)) for Borel sets B. A transformation theorem for . is a result which gives conditions on T under which .. is absolutely continuous with respect to ., and which gives a formula for the corresponding Radon-Nikodym derivative (RND) when these conditions hold.

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Absolute Continuity of the Measure States in a Branching Model with Catalysts,e variances have . with respect to Lebesgue measure, that is, roughly speaking,. for some random density function .(t)=.(t,·). Results of this type are established in Dawson and Hochberg (1979), Roelly-Coppoletta (1986), Wulfsohn (1986), Konno and Shiga (1988), and Tribe (1989).

符合你规定

,,, is not a Semimartingale,ters naturally into the study of the Brownian excursion filtration (see Rogers & Walsh [1],[2], and Walsh [4]). In [2], it was necessary to consider the occupation density of the process .. ≡ .(..), which would have been easy if . were a semimartingale; it is not, and the aim of this paper is to prove this.

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Progress in Probabilityhttp://image.papertrans.cn/s/image/864978.jpg