Displaying similar documents to “The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group”

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...

On the exponential Orlicz norms of stopped Brownian motion

Goran Peškir (1996)

Studia Mathematica

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Necessary and sufficient conditions are found for the exponential Orlicz norm (generated by ψ p ( x ) = e x p ( | x | p ) - 1 with 0 < p ≤ 2) of m a x 0 t τ | B t | or | B τ | to be finite, where B = ( B t ) t 0 is a standard Brownian motion and τ is a stopping time for B. The conditions are in terms of the moments of the stopping time τ. For instance, we find that m a x 0 t τ | B t | ψ 1 < as soon as E ( τ k ) = O ( C k k k ) for some constant C > 0 as k → ∞ (or equivalently τ ψ 1 < ). In particular, if τ ∼ Exp(λ) or | N ( 0 , σ 2 ) | then the last condition is satisfied, and we obtain m a x 0 t τ | B t | ψ 1 K E ( τ ) with some universal constant...