Extremes of standard multifractional Brownian motion

Long Bai

doi:10.1016/j.spl.2019.108697

Extremes of standard multifractional Brownian motion

Long Bai^*

^*Corresponding author for this work

Department of Financial and Actuarial Mathematics

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

Abstract

Let SMB_H(t),t∈(0,∞) be a standard multifractional Brownian motion(smBm), where H(t)∈(0,1) is a function of t. In this paper we derive the exact asymptotics of Psupt∈[T₁,T₂]SMB_H(t)>u,u→∞for constants T₁,T₂≥0 and several forms of H(t).

Original language	English
Article number	108697
Journal	Statistics and Probability Letters
Volume	159
DOIs	https://doi.org/10.1016/j.spl.2019.108697
Publication status	Published - Apr 2020

Keywords

Exact asymptotics
Multifractional Brownian motion
Pickands constants
Supremum

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10.1016/j.spl.2019.108697

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Bai, L. (2020). Extremes of standard multifractional Brownian motion. Statistics and Probability Letters, 159, Article 108697. https://doi.org/10.1016/j.spl.2019.108697

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abstract = "Let SMBH(t),t∈(0,∞) be a standard multifractional Brownian motion(smBm), where H(t)∈(0,1) is a function of t. In this paper we derive the exact asymptotics of Psupt∈[T1,T2]SMBH(t)>u,u→∞for constants T1,T2≥0 and several forms of H(t).",

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N2 - Let SMBH(t),t∈(0,∞) be a standard multifractional Brownian motion(smBm), where H(t)∈(0,1) is a function of t. In this paper we derive the exact asymptotics of Psupt∈[T1,T2]SMBH(t)>u,u→∞for constants T1,T2≥0 and several forms of H(t).

AB - Let SMBH(t),t∈(0,∞) be a standard multifractional Brownian motion(smBm), where H(t)∈(0,1) is a function of t. In this paper we derive the exact asymptotics of Psupt∈[T1,T2]SMBH(t)>u,u→∞for constants T1,T2≥0 and several forms of H(t).

KW - Exact asymptotics

KW - Multifractional Brownian motion

KW - Pickands constants

KW - Supremum

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ER -

Extremes of standard multifractional Brownian motion

Abstract

Keywords

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