Eigenvalue Expansions for Brownian Motion with an Application to Occupation Times
نویسندگان
چکیده
منابع مشابه
Eigenvalue Expansions for Brownian Motion with an Application to Occupation Times
Let B be a Borel subset of R with finite volume. We give an eigenvalue expansion for the transition densities of Brownian motion killed on exiting B. Let A1 be the time spent by Brownian motion in a closed cone with vertex 0 until time one. We show that limu→0 logP (A1 < u)/ log u = 1/ξ where ξ is defined in terms of the first eigenvalue of the Laplacian in a compact domain. Eigenvalues of the ...
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Advective skew dispersion is a natural Markov process defined by a diffusion with drift across an interface of jump discontinuity in a piecewise constant diffusion coefficient. In the absence of drift this process may be represented as a function of α-skew Brownian motion for a uniquely determined value of α = α∗; see Ramirez, Thomann, Waymire, Haggerty and Wood (2006). In the present paper the...
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 1996
ISSN: 1083-6489
DOI: 10.1214/ejp.v1-3