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Self-intersection local time for Gaussian '(d)-processes: Existence, path continuity and examples

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  • Bojdecki, Tomasz
  • Gorostiza, Luis G.

Abstract

In this paper we develop a criterion for existence or non-existence of self-intersection local time (SILT) for a wide class of Gaussian '(d)-valued processes, we show that quite generally the SILT process has continuous paths, and we give several examples which illustrate existence of SILT for different ranges of dimensions (e.g., d

Suggested Citation

  • Bojdecki, Tomasz & Gorostiza, Luis G., 1995. "Self-intersection local time for Gaussian '(d)-processes: Existence, path continuity and examples," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 191-226, December.
    • Handle: RePEc:eee:spapps:v:60:y:1995:i:2:p:191-226
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    References listed on IDEAS

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    1. Bojdecki, Tomasz & Jakubowski, Jacek, 1989. "Ito stochastic integral in the dual of a nuclear space," Journal of Multivariate Analysis, Elsevier, vol. 31(1), pages 40-58, October.
    2. Imkeller, Peter & Perez-Abreu, Victor & Vives, Josep, 1995. "Chaos expansions of double intersection local time of Brownian motion in and renormalization," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 1-34, March.
    3. Adler, Robert J. & Lewin, Marica, 1992. "Local time and Tanaka formulae for super Brownian and super stable processes," Stochastic Processes and their Applications, Elsevier, vol. 41(1), pages 45-67, May.
    4. Bojdecki, Tomasz & Jakubowski, Jacek, 1990. "Stochastic integration for inhomogeneous Wiener process in the dual of a nuclear space," Journal of Multivariate Analysis, Elsevier, vol. 34(2), pages 185-210, August.
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    Cited by:

    1. Talarczyk, Anna, 2001. "Self-intersection local time of order k for Gaussian processes in," Stochastic Processes and their Applications, Elsevier, vol. 96(1), pages 17-72, November.
    2. Gorostiza, Luis G. & Todorova, Ekaterina, 1999. "Self-intersection local time of an -valued process involving motions of two types," Stochastic Processes and their Applications, Elsevier, vol. 81(2), pages 271-298, June.
    3. Dawson, Donald A. & Hochberg, Kenneth J. & Vinogradov, Vladimir, 1996. "High-density limits of hierarchically structured branching-diffusing populations," Stochastic Processes and their Applications, Elsevier, vol. 62(2), pages 191-222, July.
    4. Bojdecki, Tomasz & Jakubowski, Jacek, 1999. "Invariant measures for generalized Langevin equations in conuclear space," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 1-24, November.

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