The supremum of brownian local times on Hölder curves
Richard F. Bass, Krzysztof Burdzy (2001)
Annales de l'I.H.P. Probabilités et statistiques
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Richard F. Bass, Krzysztof Burdzy (2001)
Annales de l'I.H.P. Probabilités et statistiques
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Wendelin Werner (2004)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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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...
Kijung Lee, Carl Mueller, Jie Xiong (2009)
Annales de l'I.H.P. Probabilités et statistiques
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For a superprocess under a stochastic flow in one dimension, we prove that it has a density with respect to the Lebesgue measure. A stochastic partial differential equation is derived for the density. The regularity of the solution is then proved by using Krylov’s -theory for linear SPDE.
Sanjar Aspandiiarov, Roudolf Iasnogorodski (1999)
Annales de l'I.H.P. Probabilités et statistiques
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