As in preceding papers in
which we studied the limits of penalized 1-dimensional Wiener
measures with certain functionals Γt, we obtain here the
existence of the limit, as t → ∞, 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}≥ 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.