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

Abstract

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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.

How to cite

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Roynette, 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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