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On the semimartingale representation of reflecting Brownian motion in a cusp
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  • Published: December 1993

On the semimartingale representation of reflecting Brownian motion in a cusp

  • R. Dante DeBlassie1 &
  • Ellen H. Toby1 

Probability Theory and Related Fields volume 94, pages 505–524 (1993)Cite this article

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Summary

LetC be the symmetric cusp {(x, y)∈ℝ2:−x β≦y≦x β,x≧0} where β>1. In this paper we decide whether or not reflecting Brownian motion inC has a semimartingale representation. Here the reflecting Brownian motion has directions of reflection that make constant angles with the unit inward normals to the boundary. Our results carry through for a wide class of asymmetric cusps too.

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References

  1. DeBlassie, R.D.: Explicit semimartingale representation of Brownian motion in a wedge. Stochastic Processes Appl.34, 67–97 (1990)

    Google Scholar 

  2. DeBlassie, R.D., Toby, E.H.: Reflecting Brownian motion in a cusp. Trans. Am. Math. Soc. (to appear 1993)

  3. Lions, P.L., Sznitman, A.S.: Stochastic differential equations with reflecting boundary conditions. Commun. Pure Appl. Math.37, 511–537 (1984)

    Google Scholar 

  4. Rogers, L.C.G., Williams, D.: Diffusions, Markov processes, and martingales, vol. 2: Itô calculus. Chichester: Wiley 1987

    Google Scholar 

  5. Stricker, C.: Quasimartingales, martingales locales, semimartingales, et filtrations naturelles. Z. Wahrscheinlichkeitstheor. Verw. Geb.39, 55–64 (1977)

    Google Scholar 

  6. Varadhan, S.R.S., Williams, R.J.: Brownian motion in a wedge with oblique reflection. Commun. Pure Appl. Math.38, 405–443 (1985)

    Google Scholar 

  7. Watanabe, S.: On stochastic differential equations for mutli-dimensional diffusion processes with boundary conditions. J. Math. Kyoto Univ.11, 169–180 (1971)

    Google Scholar 

  8. Williams, R.J.: Reflected Brownian motion in a wedge: semimartingale property. Z. Wahrscheinlichkeitstheor. Verw. Geb.69, 161–176 (1985)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Texas A & M University, 77843, College Station, TX, USA

    R. Dante DeBlassie & Ellen H. Toby

Authors
  1. R. Dante DeBlassie
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  2. Ellen H. Toby
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Dante DeBlassie, R., Toby, E.H. On the semimartingale representation of reflecting Brownian motion in a cusp. Probab. Th. Rel. Fields 94, 505–524 (1993). https://doi.org/10.1007/BF01192561

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  • Received: 06 December 1991

  • Revised: 19 May 1992

  • Issue Date: December 1993

  • DOI: https://doi.org/10.1007/BF01192561

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Mathematics Subject Classification (1985)

  • 60J65
  • 60J60
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