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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Mario V. Wüthrich (1999)
Annales de l'I.H.P. Probabilités et statistiques
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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.
Richard F. Bass, Krzysztof Burdzy (2001)
Annales de l'I.H.P. Probabilités et statistiques
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Fabrice Baudoin, Neil O’Connell (2011)
Annales de l'I.H.P. Probabilités et statistiques
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We consider exponential functionals of a brownian motion with drift in ℝ, defined via a collection of linear functionals. We give a characterisation of the Laplace transform of their joint law as the unique bounded solution, up to a constant factor, to a Schrödinger-type partial differential equation. We derive a similar equation for the probability density. We then characterise all diffusions which can be interpreted as having the law of the brownian motion with drift conditioned on...
David Hobson (1994)
Annales de l'I.H.P. Probabilités et statistiques
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