Brownian motion with partial information1

Terry R. McConnell

doi:10.1090/S0002-9947-1982-0654858-5

Brownian motion with partial information1

Terry R. McConnell

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

1 Scopus citations

Abstract

We study the following problem concerning stopped N-dimensional Brownian motion: Compute the maximal function of the process, ignoring those times when it is in some fixed region R. Suppose this modified maximal function belongs to L^qFor what regions R can we conclude that the unrestricted maximal function belongs to L^qc! A sufficient condition on R is that there exist p > q and a function w, harmonic in /?, such that \x\^p^ u(x) < C\x\^p+ C, x Çz R, for some constant C. We give applications to analytic and harmonic functions, and to weak inequalities for exit times.

Original language	English (US)
Pages (from-to)	719-731
Number of pages	13
Journal	Transactions of the American Mathematical Society
Volume	271
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-1982-0654858-5
State	Published - Jun 1982
Externally published	Yes

Keywords

Brownian motion
Exit time
Hardy space
Harmonic majorization
Maximal function

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9947-1982-0654858-5

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AB - We study the following problem concerning stopped N-dimensional Brownian motion: Compute the maximal function of the process, ignoring those times when it is in some fixed region R. Suppose this modified maximal function belongs to LqFor what regions R can we conclude that the unrestricted maximal function belongs to Lqc! A sufficient condition on R is that there exist p > q and a function w, harmonic in /?, such that \x\p^ u(x) < C\x\p+ C, x Çz R, for some constant C. We give applications to analytic and harmonic functions, and to weak inequalities for exit times.

KW - Brownian motion

KW - Exit time

KW - Hardy space

KW - Harmonic majorization

KW - Maximal function

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JF - Transactions of the American Mathematical Society

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Brownian motion with partial information1

Abstract

Keywords

ASJC Scopus subject areas

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