On the joint asymptotic behaviours of ranked heights of Brownian excursions
نویسنده
چکیده
1 A. Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13–15, P.O.B. 127, Budapest, H–1364, Hungary. Research supported by the Hungarian National Foundation for Scientific Research, Grant No. T 019346 and T 029621. E-mail: [email protected] 2 Laboratoire de Probabilités et Modèles Aléatoires, CNRS UMR–7599, Université Paris VI, Tour 56, 3e étage, 4 Place Jussieu, F–75252 Paris cedex 05, France. E-mail: [email protected]
منابع مشابه
Lengths and heights of random walk excursions
Consider a simple symmetric random walk on the line. The parts of the random walk between consecutive returns to the origin are called excursions. The heights and lengths of these excursions can be arranged in decreasing order. In this paper we give the exact and limiting distributions of these ranked quantities. These results are analogues of the corresponding results of Pitman and Yor [10, 11...
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The distribution of the sequence of ranked maximum and minimum values attained during excursions of a standard Brownian bridge Bbr t 0 ≤ t ≤ 1 is described. The height Mbr+ j of the jth highest maximum over a positive excursion of the bridge has the same distribution as Mbr+ 1 /j, where the distribution of Mbr+ 1 = sup0≤t≤1 Bbr t is given by Lévy’s formula P Mbr+ 1 > x = e−2x 2 . The probabilit...
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The distribution of the sequence of ranked maximum and minimum values attained during excursions of a standard Brownian bridge (Bbr t ; 0 t 1) is described. The height M j of the jth highest maximum over a positive excursion of the bridge has the same distribution as M 1 =j, where the distribution of M 1 = sup0 t 1B br t is given by L evy's formula P (M br+ 1 > x) = e 2x . The probability densi...
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