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Self-intersection local time of order k for Gaussian processes in

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  • Talarczyk, Anna

Abstract

We study existence and continuity of self-intersection local time of any order of Gaussian processes. In particular, we give results for Wiener and Ornstein-Uhlenbeck processes. We study processes associated with several classes of covariances, which arise in examples mainly as fluctuation limits of particle systems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:96:y:2001:i:1:p:17-72
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    References listed on IDEAS

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    1. 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.
    2. Peszat, Szymon & Zabczyk, Jerzy, 1997. "Stochastic evolution equations with a spatially homogeneous Wiener process," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 187-204, December.
    3. 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.
    4. Dawson, Donald A. & Salehi, Habib, 1980. "Spatially homogeneous random evolutions," Journal of Multivariate Analysis, Elsevier, vol. 10(2), pages 141-180, June.
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    1. T. Bojdecki & Luis G. Gorostiza & A. Talarczyk, 2004. "Functional Limit Theorems for Occupation Time Fluctuations of Branching Systems in the Cases of Large and Critical Dimensions," RePAd Working Paper Series lrsp-TRS404, Département des sciences administratives, UQO.
    2. Bojdecki, T. & Gorostiza, L.G. & Talarczyk, A., 2006. "Limit theorems for occupation time fluctuations of branching systems II: Critical and large dimensions," Stochastic Processes and their Applications, Elsevier, vol. 116(1), pages 19-35, January.
    3. T. Bojdecki & L. G. Gorostiza & A. Talarczyk, 2004. "Fractional Brownian Density Process and Its Self-Intersection Local Time of Order k," Journal of Theoretical Probability, Springer, vol. 17(3), pages 717-739, July.
    4. Bojdecki, Tomasz & Talarczyk, Anna, 2005. "Particle picture approach to the self-intersection local time of density processes in," Stochastic Processes and their Applications, Elsevier, vol. 115(3), pages 449-479, March.

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