A note on the range of stochastic processes

Maher Boudabra; Binghao Wu

doi:10.1214/24-ECP653

A note on the range of stochastic processes

Maher Boudabra
, Binghao Wu

Department of Mathematics

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

Abstract

A Brownian motion with drift is simply a process V^η t of the form (Formula Presented) where B_t is a standard Brownian motion and η > 0. In [7], the authors showed that the underlying range (Formula Presented) is equivalent to ηt a.e in the long run, i.e (Formula Presented) In this paper, we show that (0.1) follows from a deterministic property. More precisely, we show that the long run behavior of the range of a (deterministic) function is obtainable straightaway from that of the function itself.

Original language	English
Article number	2
Journal	Electronic Communications in Probability
Volume	30
DOIs	https://doi.org/10.1214/24-ECP653
State	Published - 2025

Bibliographical note

Publisher Copyright:
© 2025, Institute of Mathematical Statistics. All rights reserved.

Keywords

Brownian motion with drift
stochastic processes

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/24-ECP653

Cite this

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AB - A Brownian motion with drift is simply a process Vη t of the form (Formula Presented) where Bt is a standard Brownian motion and η > 0. In [7], the authors showed that the underlying range (Formula Presented) is equivalent to ηt a.e in the long run, i.e (Formula Presented) In this paper, we show that (0.1) follows from a deterministic property. More precisely, we show that the long run behavior of the range of a (deterministic) function is obtainable straightaway from that of the function itself.

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KW - stochastic processes

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A note on the range of stochastic processes

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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