On Paul Lévy’s arc sine law and Shiga-Watanabe’s time inversion result

• Autorzy: Graversen S. E. , Vuolle-Apiala J.
• Języki publikacji: EN

Abstrakty

EN

Let ((X_t), P) be a symmetric real-valued H-self-similar diffusion starting at 0. We characterize the distributions of A_t, the time spent on (0, ∞) before time t, and g_t, the time of the last visit to 0 before t. This gives a simple new proof to well-known results in cluding P. Lévy’s arc sine law for Brownian motion and Brownian bridge and similar results for symmetrized Bessel processes. Our focus is more on simplicity of proofs than on novelty of results. Section 3 contains a generalization of T. Shiga’s and S. Watanabe’s theorem on time inversion for Bessel processes. We show that their result holds also for symmetrized Bessel processes.

Słowa kluczowe

EN

Bessel processes; time inversion; Brownian motion

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2000
• Tom: Vol. 20, Fasc. 1
• Strony: 63--73
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Graversen S. E.

• Department of Mathematics, University of Aarhus, Ny Munkegade, 8000 Aarhus C, Denmark

autor

Vuolle-Apiala J.

• Department of Mathematics, University of Helsinki, P.O. Box 4, 00014 University of Helsinki, Finland

Bibliografia

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