Some Martingales Related to the Integral of Brownian Motion. Applications to the Passage Times and Transience期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Some Martingales Related to the Integral of Brownian Motion. Applications to the Passage Times and Transience

Authors:	Aimé Lachal

Affiliation:	(1) Laboratoire de Probabilités, U.F.R. de Mathématiques et Informatique, Université Claude Bernard, Lyon 1, 43 boulevard du 11 Novembre 1918, F-69622 Villeurbanne Cedex, France

Abstract:	Let (B_t)_t0 be the standard linear Brownian motion started at y and set (X_t, B_t). In this paper we introduce some martingales related to the Markov process (U_t)_t0, which allow us to calculate explicitly the probability laws of several passage times associated to U in a probabilistic way. With the aid of an appropriate supermartingale, we also establish the transience of the process (U_t)_t0.

Keywords:	Martingales Markov times Laplace– Kontorovich– Lebedev Mellin transforms
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