Derivatives of local times for some Gaussian fields II

Minhao Hong; Fangjun Xu

doi:10.1016/j.spl.2021.109063

Derivatives of local times for some Gaussian fields II

Minhao Hong
, Fangjun Xu^*

^*Corresponding author for this work

School of Statistics

East China Normal University

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

4 Scopus citations

Abstract

Given a (2,d)-Gaussian field Z={Z(t,s)=X_t^H₁−X˜_s^H₂,s,t≥0},where X^H₁ and X˜^H₂ are independent d-dimensional centered Gaussian processes satisfying certain properties, we will give a necessary condition for existence of derivatives of the local time of Z at x∈R^d, this condition is also sufficient when X^H₁ and X˜^H₂ satisfy the local nondeterminism property.

Original language	English
Article number	109063
Journal	Statistics and Probability Letters
Volume	172
DOIs	https://doi.org/10.1016/j.spl.2021.109063
State	Published - May 2021

Keywords

Derivatives of local time
Gaussian fields
Necessary condition

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10.1016/j.spl.2021.109063

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title = "Derivatives of local times for some Gaussian fields II",

abstract = "Given a (2,d)-Gaussian field Z=\{Z(t,s)=XtH1−X˜sH2,s,t≥0\},where XH1 and X˜H2 are independent d-dimensional centered Gaussian processes satisfying certain properties, we will give a necessary condition for existence of derivatives of the local time of Z at x∈Rd, this condition is also sufficient when XH1 and X˜H2 satisfy the local nondeterminism property.",

keywords = "Derivatives of local time, Gaussian fields, Necessary condition",

author = "Minhao Hong and Fangjun Xu",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

year = "2021",

month = may,

doi = "10.1016/j.spl.2021.109063",

language = "英语",

volume = "172",

journal = "Statistics and Probability Letters",

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AU - Hong, Minhao

AU - Xu, Fangjun

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N2 - Given a (2,d)-Gaussian field Z={Z(t,s)=XtH1−X˜sH2,s,t≥0},where XH1 and X˜H2 are independent d-dimensional centered Gaussian processes satisfying certain properties, we will give a necessary condition for existence of derivatives of the local time of Z at x∈Rd, this condition is also sufficient when XH1 and X˜H2 satisfy the local nondeterminism property.

AB - Given a (2,d)-Gaussian field Z={Z(t,s)=XtH1−X˜sH2,s,t≥0},where XH1 and X˜H2 are independent d-dimensional centered Gaussian processes satisfying certain properties, we will give a necessary condition for existence of derivatives of the local time of Z at x∈Rd, this condition is also sufficient when XH1 and X˜H2 satisfy the local nondeterminism property.

KW - Derivatives of local time

KW - Gaussian fields

KW - Necessary condition

UR - https://www.scopus.com/pages/publications/85101651876

U2 - 10.1016/j.spl.2021.109063

DO - 10.1016/j.spl.2021.109063

M3 - 文章

AN - SCOPUS:85101651876

SN - 0167-7152

VL - 172

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

M1 - 109063

ER -

Derivatives of local times for some Gaussian fields II

Abstract

Keywords

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