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

Aimé Lachal ()
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Aimé Lachal: Université Claude Bernard

Journal of Theoretical Probability, 1998, vol. 11, issue 1, 127-156

Abstract: Abstract Let (B t) t≥0 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) t≥0, 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) t≥0.

Keywords: Martingales; Markov times; Laplace–Kontorovich–Lebedev Mellin transforms (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1021646925303

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