Some changes of probabilities related to a geometric Brownian motion version of Pitman's  theorem.

Matsumoto, Hiroyuki; Yor, Marc

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Penalisations of multidimensional Brownian motion, VI

Bernard Roynette, Pierre Vallois, Marc Yor (2009)

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As in preceding papers in which we studied the limits of penalized 1-dimensional Wiener measures with certain functionals Γ, we obtain here the existence of the limit, as → ∞, of -dimensional Wiener measures penalized by a function of the maximum up to time of the Brownian winding process (for ), or in 2 dimensions for Brownian motion prevented to exit a cone before time . Various extensions of these multidimensional penalisations are studied, and the limit laws...