Local times of fractional Brownian sheets

Yimin Xiao; Tusheng Zhang

doi:10.1007/s004400200210

Local times of fractional Brownian sheets

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

Abstract

Let B0H = {B0H (t), t ∈ ℝ+N} be a real-valued fractional Brownian sheet. Consider the (N, d) Gaussian random field BH defined by BH (t) = (B1H (t), ..., BdH (t)) (t ∈ ℝ+N), where B1H, ..., BdH are independent copies of B0H. In this paper, the existence and joint continuity of the local times of BH are established.

Original language	English
Pages (from-to)	204-226
Number of pages	22
Journal	Probability Theory and Related Fields
Volume	124
Issue number	2
DOIs	https://doi.org/10.1007/s004400200210
Publication status	Published - Oct 2002

Keywords

Fractional Brownian motion
Fractional Brownian sheet
Joint continuity
Local times

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10.1007/s004400200210

http://dx.doi.org/10.1007/s004400200210

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@article{80412935b5064102a5564163aa701708,

title = "Local times of fractional Brownian sheets",

abstract = "Let B0H = {B0H (t), t ∈ ℝ+N} be a real-valued fractional Brownian sheet. Consider the (N, d) Gaussian random field BH defined by BH (t) = (B1H (t), ..., BdH (t)) (t ∈ ℝ+N), where B1H, ..., BdH are independent copies of B0H. In this paper, the existence and joint continuity of the local times of BH are established.",

keywords = "Fractional Brownian motion, Fractional Brownian sheet, Joint continuity, Local times",

author = "Yimin Xiao and Tusheng Zhang",

year = "2002",

month = oct,

doi = "10.1007/s004400200210",

language = "English",

volume = "124",

pages = "204--226",

journal = "Probability Theory and Related Fields",

issn = "0178-8051",

publisher = "Springer Nature",

number = "2",

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TY - JOUR

T1 - Local times of fractional Brownian sheets

AU - Xiao, Yimin

AU - Zhang, Tusheng

PY - 2002/10

Y1 - 2002/10

N2 - Let B0H = {B0H (t), t ∈ ℝ+N} be a real-valued fractional Brownian sheet. Consider the (N, d) Gaussian random field BH defined by BH (t) = (B1H (t), ..., BdH (t)) (t ∈ ℝ+N), where B1H, ..., BdH are independent copies of B0H. In this paper, the existence and joint continuity of the local times of BH are established.

AB - Let B0H = {B0H (t), t ∈ ℝ+N} be a real-valued fractional Brownian sheet. Consider the (N, d) Gaussian random field BH defined by BH (t) = (B1H (t), ..., BdH (t)) (t ∈ ℝ+N), where B1H, ..., BdH are independent copies of B0H. In this paper, the existence and joint continuity of the local times of BH are established.

KW - Fractional Brownian motion

KW - Fractional Brownian sheet

KW - Joint continuity

KW - Local times

U2 - 10.1007/s004400200210

DO - 10.1007/s004400200210

M3 - Article

SN - 0178-8051

VL - 124

SP - 204

EP - 226

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 2

ER -

Local times of fractional Brownian sheets

Abstract

Keywords

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