Sharp integrability for Brownian motion in parabola-shaped regions

Rodrigo Bañuelos; Tom Carroll

doi:10.1016/j.jfa.2004.05.006

Sharp integrability for Brownian motion in parabola-shaped regions

Rodrigo Bañuelos
, Tom Carroll

School of Mathematical Sciences

Purdue University

Research output: Contribution to journal › Article › peer-review

Abstract

We study the sharp order of integrability of the exit position of Brownian motion from the planar domains P_α = {(x, y) ∈ ℝ × ℝ: x > 0, y < Ax^α}, 0 < α < 1. Together with some simple good- λ type arguments, this implies the order of integrability for the exit time of these domains; a result first proved for α = 1/2 by Bañuelos et al. (Ann. Probab. 29 (2001) 882) and for general α by Li (Ann. Probab. 31 (2003) 1078). A sharp version of this result is also proved in higher dimensions.

Original language	English
Pages (from-to)	219-253
Number of pages	35
Journal	Journal of Functional Analysis
Volume	218
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2004.05.006
Publication status	Published - 1 Jan 2005

Keywords

Brownian motion
Conformal mapping
Harmonic measure

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10.1016/j.jfa.2004.05.006

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abstract = "We study the sharp order of integrability of the exit position of Brownian motion from the planar domains Pα = \{(x, y) ∈ ℝ × ℝ: x > 0, y < Axα\}, 0 < α < 1. Together with some simple good- λ type arguments, this implies the order of integrability for the exit time of these domains; a result first proved for α = 1/2 by Ba{\~n}uelos et al. (Ann. Probab. 29 (2001) 882) and for general α by Li (Ann. Probab. 31 (2003) 1078). A sharp version of this result is also proved in higher dimensions.",

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AU - Carroll, Tom

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N2 - We study the sharp order of integrability of the exit position of Brownian motion from the planar domains Pα = {(x, y) ∈ ℝ × ℝ: x > 0, y < Axα}, 0 < α < 1. Together with some simple good- λ type arguments, this implies the order of integrability for the exit time of these domains; a result first proved for α = 1/2 by Bañuelos et al. (Ann. Probab. 29 (2001) 882) and for general α by Li (Ann. Probab. 31 (2003) 1078). A sharp version of this result is also proved in higher dimensions.

AB - We study the sharp order of integrability of the exit position of Brownian motion from the planar domains Pα = {(x, y) ∈ ℝ × ℝ: x > 0, y < Axα}, 0 < α < 1. Together with some simple good- λ type arguments, this implies the order of integrability for the exit time of these domains; a result first proved for α = 1/2 by Bañuelos et al. (Ann. Probab. 29 (2001) 882) and for general α by Li (Ann. Probab. 31 (2003) 1078). A sharp version of this result is also proved in higher dimensions.

KW - Brownian motion

KW - Conformal mapping

KW - Harmonic measure

UR - https://www.scopus.com/pages/publications/8844283460

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VL - 218

SP - 219

EP - 253

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 1

ER -

Sharp integrability for Brownian motion in parabola-shaped regions

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Keywords

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