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

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  • Bass, Richard

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.

Suggested Citation

  • Bass, Richard, 1984. "Joint continuity and representations of additive functionals of d-dimensional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 17(2), pages 211-227, July.
    • Handle: RePEc:eee:spapps:v:17:y:1984:i:2:p:211-227
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    Cited by:

    1. Shieh, Narn-Rueih, 1995. "Some self-similar processes related to local times," Statistics & Probability Letters, Elsevier, vol. 24(3), pages 213-218, August.
    2. Khoshnevisan, Davar, 1996. "Deviation inequalities for continuous martingales," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 17-30, December.
    3. Uemura, H., 2008. "Generalized positive continuous additive functionals of multidimensional Brownian motion and their associated Revuz measures," Stochastic Processes and their Applications, Elsevier, vol. 118(10), pages 1870-1891, October.

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