Penalisations of multidimensional brownian motion, VI

Roynette, Bernard; Vallois, Pierre; Yor, Marc

ESAIM: Probability and Statistics, Tome 13 (2009), pp. 152-180.

As in preceding papers in which we studied the limits of penalized 1-dimensional Wiener measures with certain functionals ${\Gamma }_t$, we obtain here the existence of the limit, as $t\to \infty$, of $d$-dimensional Wiener measures penalized by a function of the maximum up to time $t$ of the brownian winding process (for $d=2$), or in $d$ $\ge$ 2 dimensions for brownian motion prevented to exit a cone before time $t$. Various extensions of these multidimensional penalisations are studied, and the limit laws are described. Throughout this paper, the skew-product decomposition of $d$-dimensional brownian motion plays an important role.

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