Joint continuity and representations of additive functionals of d-dimensional Brownian motion

Richard Bass

Stochastic Processes and their Applications, 1984, vol. 17, issue 2, 211-227

Abstract: Conditions are given on a family of measures {[mu]a, 0[less-than-or-equals, slant]a[less-than-or-equals, slant]1} so that the corresponding family {Aat, 0[less-than-or-equals, slant]a[less-than-or-equals, slant]1} of additive functionals of d-dimensional Brownian motion will be jointly continuous in a and t, a.s. This is then used to give a d-dimensional analogue to the representation At = [is proportional to] Lyt[mu](dy) that is valid for one-dimensional Brownian motion, where Lyt is local time at y. In place of local times at points, local times at hyperplanes are used.

Keywords: additive; functionals; Radon; transform; local; times; potentials; stochastic; integrals (search for similar items in EconPapers)
Date: 1984
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Citations: View citations in EconPapers (3)

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