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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title = "Extremes of standard multifractional Brownian motion",

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).",

keywords = "Exact asymptotics, Multifractional Brownian motion, Pickands constants, Supremum",

author = "Long Bai",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier B.V.",

year = "2020",

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doi = "10.1016/j.spl.2019.108697",

language = "English",

volume = "159",

journal = "Statistics and Probability Letters",

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PY - 2020/4

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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

UR - https://www.scopus.com/pages/publications/85077746598

U2 - 10.1016/j.spl.2019.108697

DO - 10.1016/j.spl.2019.108697

M3 - Article

AN - SCOPUS:85077746598

SN - 0167-7152

VL - 159

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

M1 - 108697

ER -

Extremes of standard multifractional Brownian motion

Abstract

Keywords

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