On maximum increase and decrease of brownian motion
Paavo Salminen, Pierre Vallois (2007)
Annales de l'I.H.P. Probabilités et statistiques
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Paavo Salminen, Pierre Vallois (2007)
Annales de l'I.H.P. Probabilités et statistiques
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Marc Arnaudon, Thomas Simon (2005)
Annales de l’institut Fourier
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We study the rate of concentration of a Brownian bridge in time one around the corresponding geodesical segment on a Cartan-Hadamard manifold with pinched negative sectional curvature, when the distance between the two extremities tends to infinity. This improves on previous results by A. Eberle, and one of us . Along the way, we derive a new asymptotic estimate for the logarithmic derivative of the heat kernel on such manifolds, in bounded time and with one...
B. Roynette, P. Vallois, M. Yor (2009)
Annales de l'I.H.P. Probabilités et statistiques
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Limiting laws, as →∞, for brownian motion penalised by the longest length of excursions up to , or up to the last zero before , or again, up to the first zero after , are shown to exist, and are characterized.
David Hobson (1994)
Annales de l'I.H.P. Probabilités et statistiques
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Peter Mörters (2001)
Annales de l'I.H.P. Probabilités et statistiques
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