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Itô's theory of excursion point processes and its developments

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  • Watanabe, Shinzo

Abstract

Itô's theory of excursion point processes is reviewed and the following topics are discussed: Application of the theory to one-dimensional diffusion processes on half-intervals satisfying Feller's boundary conditions, and its multi-dimensional extension, i.e., the application of the theory to multi-dimensional diffusion processes satisfying Wentzell's boundary conditions.

Suggested Citation

  • Watanabe, Shinzo, 2010. "Itô's theory of excursion point processes and its developments," Stochastic Processes and their Applications, Elsevier, vol. 120(5), pages 653-677, May.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:5:p:653-677
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    Cited by:

    1. Anna Ananova & Rama Cont & Renyuan Xu, 2020. "Model-free Analysis of Dynamic Trading Strategies," Papers 2011.02870, arXiv.org, revised Aug 2023.
    2. Bertoin, Jean, 2010. "A limit theorem for trees of alleles in branching processes with rare neutral mutations," Stochastic Processes and their Applications, Elsevier, vol. 120(5), pages 678-697, May.
    3. Le Gall, Jean-François, 2010. "Itô's excursion theory and random trees," Stochastic Processes and their Applications, Elsevier, vol. 120(5), pages 721-749, May.

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