# Penalisations of multidimensional Brownian motion, VI

Bernard Roynette; Pierre Vallois; Marc Yor

ESAIM: Probability and Statistics (2009)

- Volume: 13, page 152-180
- ISSN: 1292-8100

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topRoynette, Bernard, Vallois, Pierre, and Yor, Marc. "Penalisations of multidimensional Brownian motion, VI." ESAIM: Probability and Statistics 13 (2009): 152-180. <http://eudml.org/doc/250673>.

@article{Roynette2009,

abstract = {
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.
},

author = {Roynette, Bernard, Vallois, Pierre, Yor, Marc},

journal = {ESAIM: Probability and Statistics},

keywords = {Skew-product
decomposition; Brownian windings; Dirichlet problem; spectral
decomposition; skew-product decomposition; spectral decomposition},

language = {eng},

month = {6},

pages = {152-180},

publisher = {EDP Sciences},

title = {Penalisations of multidimensional Brownian motion, VI},

url = {http://eudml.org/doc/250673},

volume = {13},

year = {2009},

}

TY - JOUR

AU - Roynette, Bernard

AU - Vallois, Pierre

AU - Yor, Marc

TI - Penalisations of multidimensional Brownian motion, VI

JO - ESAIM: Probability and Statistics

DA - 2009/6//

PB - EDP Sciences

VL - 13

SP - 152

EP - 180

AB -
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.

LA - eng

KW - Skew-product
decomposition; Brownian windings; Dirichlet problem; spectral
decomposition; skew-product decomposition; spectral decomposition

UR - http://eudml.org/doc/250673

ER -

## References

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