On the remarkable distributions of maxima of some fragments of the standard reflecting random walk and Brownian motion

• Autorzy: Fujita T. , Yor M.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we consider some distributions of maxima of excursions and related variables for standard random walk and Brownian motion. We discuss the infinite divisibility properties of these distributions and calculate their Lévy measures. Lastly we discuss Chung's remark related with Riemann's zeta functional equation.

Słowa kluczowe

EN

standard random walk; standard Brownian motion; excursion; meander; comeander; infinite divisibility; Lévy measure; arcsine law; Riemann zeta function

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2007
• Tom: Vol. 27, Fasc. 1
• Strony: 89--104
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Fujita T.

• Graduate School of Commerce and Management, Hitotsubashi University, Naka 2.1, Kunitachi, Tokyo 186.8601, Japan

autor

Yor M.

• Laboratoire de Probabilitbs et Moddles Alkatoires, Université Paris VI, casier 188,4, place Jussieu, 75 252 Paris cedex 05, France

Bibliografia

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• [8] T. Fujita and M. Yor, A warning about an independence property related to random Brownian scaling, this fascicle, pp. 105-108.
• [9] J. Pitman and M. Yor, Decomposition at the maximum for excursions and bridges of one-dimensional diffusions, in: Itô's Stochastic Calculus and Probability Theory, N. Ikeda, S. Watanabe, M. Fukushima, H. Kunita (Eds.), Springer, Berlin-Heidelberg-New York 1996, pp. 293-310.
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