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Asymptotics of the Persistence Exponent of Integrated Fractional Brownian Motion and Fractionally Integrated Brownian Motion

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2022Embargo end date: 01 Jan 2020Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:Theory of Probability & Its Applications, volume 67, pages 77-88 (issn: 0040-585X, eissn: 1095-7219,

Authors: Aurzada, Frank; Kilian, Martin;

doi: 10.1137/s0040585x97t990769 , 10.4213/tvp5423 , 10.48550/arxiv.2007.01254

arXiv: http://arxiv.org/abs/2007.01254

Asymptotics of the Persistence Exponent of Integrated Fractional Brownian Motion and Fractionally Integrated Brownian Motion

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Abstract

Рассматривается вероятность персистентности для интегрированного дробного броуновского движения и дробно интегрированного броуновского движения с параметром $H$. Для интегрированного дробного броуновского движения обсуждается гипотеза Молчана- Хохлова и устанавливается асимптотическое поведение показателя персистентности при $H\to0$ и при $H\to1$, находящееся в согласии с указанной гипотезой. Для дробно интегрированного броуновского движения, называемого также процессом Римана-Лиувилля, найдено асимптотическое поведение показателя персистентности при $H\to0$.

Related Organizations

TU Darmstadt
Germany

Keywords

Probability (math.PR), FOS: Mathematics, Mathematics - Probability, 60G15, 60G22

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