Displaying similar documents to “On the joint distribution of the maximum and its location for a linear diffusion”

Exponential functionals of brownian motion and class-one Whittaker functions

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...