On the exit time from a cone for brownian motion with drift

Rodolphe Garbit, Kilian Raschel

Type: Article

Publication Date: 2014-01-01

Citations: 16

DOI: https://doi.org/10.1214/ejp.v19-3169

Abstract

We investigate the tail distribution of the first exit time of Brownian motion with drift from a cone and find its exact asymptotics for a large class of cones. Our results show in particular that its exponential decreasing rate is a function of the distance between the drift and the cone, whereas the polynomial part in the asymptotics depends on the position of the drift with respect to the cone and its polar cone, and reflects the local geometry of the cone at the point where the drift is orthogonally projected.

Locations

Electronic Journal of Probability - View - PDF
arXiv (Cornell University) - View - PDF
HAL (Le Centre pour la Communication Scientifique Directe) - View - PDF
DataCite API - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Exit times from cones in ℝ n of Brownian motion	1987	R. Dante DeBlassie
+	Exit times from cones for non-homogeneous random walk with asymptotically zero drift	2008	Iain M. MacPhee Mikhail Menshikov Andrew R. Wade
+	Martin Boundary of a Space-time Brownian Motion with Drift Killed at the Boundary of a Moving Cone	2024	Sandro Franceschi
+	Angular asymptotics for multi-dimensional non-homogeneous random walks with asymptotically zero drift	2010	Iain M. MacPhee Mikhail Menshikov Andrew R. Wade
+ PDF Chat	Remark on exit times from cones in $$\mathbb{R}^n $$ of Brownian motion	1988	R. Dante De Blassie
+	Angular asymptotics for multi-dimensional non-homogeneous random walks with asymptotically zero drift	2009	Iain M. MacPhee Mikhail Menshikov Andrew R. Wade
+	Random walks with drift inside a pyramid: convergence rate for the survival probability	2022	Rodolphe Garbit Kilian Raschel
+ PDF Chat	Brownian motion in a quasi-cone	2011	Dante DeBlassie
+	Integrability properties and limit theorems for the exit time from a cone of planar Brownian motion	2013	Stavros Vakeroudis Marc Yor
+ PDF Chat	On the exit time from a cone for random walks with drift	2016	Rodolphe Garbit Kilian Raschel
+	Extremal behaviour of hitting a cone by correlated Brownian motion with drift	2016	Krzysztof Dȩbicki Enkelejd Hashorva Lanpeng Ji Tomasz Rolski
+	Extremal behaviour of hitting a cone by correlated Brownian motion with drift	2016	Krzysztof Dȩbicki Enkelejd Hashorva Lanpeng Ji Tomasz Rolski
+	Martin boundary of a killed non-centered random walk in a general cone	2020	Irina Ignatiouk-Robert
+	Cone exponents of Brownian motions with particular drifts	2019	Izumia Okada
+	The exit distribution for iterated Brownian motion in cones	2005	Rodrigo Bañuelos Dante DeBlassie
+ PDF Chat	Random walks in cones: The case of nonzero drift	2013	Jetlir Duraj
+	Probability of entering an orthant by correlated fractional Brownian motion with drift: exact asymptotics	2024	Krzysztof Dȩbicki Lanpeng Ji Svyatoslav Novikov
+	The exit distribution for iterated Brownian motion in cones	2004	Rodrigo Bañuelos Dante DeBlassie
+	Boundary behavior for random walks in cones	2018	Kilian Raschel Pierre Tarrago
+ PDF Chat	Brownian motion in cones	1997	Rodrigo Bañuelos Robert G. Smits

Works That Cite This (16)

Action	Title	Year	Authors
+	An elementary solution of Gessel's walks in the quadrant	2016	Mireille Bousquet‐Mélou
+	Extremal behavior of hitting a cone by correlated Brownian motion with drift	2018	Krzysztof Dȩbicki Enkelejd Hashorva Lanpeng Ji Tomasz Rolski
+ PDF Chat	Taming reluctant random walks in the positive quadrant	2017	Jérémie Lumbroso Marni Mishna Yann Ponty
+	3D positive lattice walks and spherical triangles	2020	Beniamin Bogosel Vincent Perrollaz Kilian Raschel Amélie Trotignon
+	Entrance laws at the origin of self-similar Markov processes in high dimensions	2020	Andreas E. Kyprianou Víctor M. Hernández Rivero Batı Şengül Ting Yang
+	Entrance laws at the origin of self-similar Markov processes in high dimensions	2018	Andreas E. Kyprianou Víctor M. Hernández Rivero Batı Şengül Ting Yang
+	Cone exponents of Brownian motions with particular drifts	2019	Izumia Okada
+ PDF Chat	Harmonic functions for singular quadrant walks	2023	Viet Hung Hoang Kilian Raschel Pierre Tarrago
+ PDF Chat	On the singular values of complex matrix Brownian motion with a matrix drift	2023	Theodoros Assiotis
+	An elementary solution of Gessel's walks in the quadrant	2015	Mireille Bousquet‐Mélou

Works Cited by This (27)

Action	Title	Year	Authors
+ PDF Chat	Brownian motion conditioned to stay in a cone	2009	Rodolphe Garbit
+	Brownian motion and stochastic calculus	1991	Jan Seidler
+ PDF Chat	Permutation model for semi-circular systems and quantum random walks	1995	Philippe Biane
+ PDF Chat	Elliptic Partial Differential Equations of Second Order	2001	David Gilbarg Neil S. Trudinger
+ PDF Chat	Remarks on the maximum principle for parabolic equations and its applications	1958	Avner Friedman
+	Analyticity at the boundary of solutions of nonlinear second‐order parabolic equations	1978	David Kinderlehrer Louis Nirenberg
+	A Brownian-Motion Model for the Eigenvalues of a Random Matrix	1962	Freeman J. Dyson
+	Exit times of Brownian motion, harmonic majorization, and Hardy spaces	1977	D. L. Burkholder
+ PDF Chat	Coincidence properties of birth and death processes	1959	Samuel Karlin James McGregor
+	Littelmann paths and brownian paths	2004	Philippe Biane Philippe Bougerol Neil O’Connell