On the quasi-everywhere regularity of the local time of one-dimensional diffusion process in Besov space

Xicheng Zhang

doi:10.1016/S0167-7152(01)00033-5

On the quasi-everywhere regularity of the local time of one-dimensional diffusion process in Besov space

Xicheng Zhang^*

^*Corresponding author for this work

Huazhong University of Science and Technology

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

3 Citations (Scopus)

Abstract

In this paper, we prove that the local time L(t,x) of one-dimensional diffusion process exists except for a set of (2,n) zero capacity for all n≥1. Moreover, we also prove that L(t,x) as a function of x∈R quasi-everywhere belongs to Besov spaces B_p,1^α for α<1/2,1<p<∞.

Original language	English
Pages (from-to)	161-169
Number of pages	9
Journal	Statistics and Probability Letters
Volume	54
Issue number	2
DOIs	https://doi.org/10.1016/S0167-7152(01)00033-5
Publication status	Published - 15 Sept 2001
Externally published	Yes

Keywords

60H10
60J55
Besov spaces
Capacity
Local times
n -parameter Ornstein-Uhlenbeck process

Access to Document

10.1016/S0167-7152(01)00033-5

Cite this

@article{2feb622d486e49b08c58ce82df2d4caa,

title = "On the quasi-everywhere regularity of the local time of one-dimensional diffusion process in Besov space",

abstract = "In this paper, we prove that the local time L(t,x) of one-dimensional diffusion process exists except for a set of (2,n) zero capacity for all n≥1. Moreover, we also prove that L(t,x) as a function of x∈R quasi-everywhere belongs to Besov spaces Bp,1α for α<1/2,1",

keywords = "60H10, 60J55, Besov spaces, Capacity, Local times, n -parameter Ornstein-Uhlenbeck process",

author = "Xicheng Zhang",

year = "2001",

month = sep,

day = "15",

doi = "10.1016/S0167-7152(01)00033-5",

language = "English",

volume = "54",

pages = "161--169",

journal = "Statistics and Probability Letters",

issn = "0167-7152",

publisher = "Elsevier B.V.",

number = "2",

}

TY - JOUR

T1 - On the quasi-everywhere regularity of the local time of one-dimensional diffusion process in Besov space

AU - Zhang, Xicheng

PY - 2001/9/15

Y1 - 2001/9/15

N2 - In this paper, we prove that the local time L(t,x) of one-dimensional diffusion process exists except for a set of (2,n) zero capacity for all n≥1. Moreover, we also prove that L(t,x) as a function of x∈R quasi-everywhere belongs to Besov spaces Bp,1α for α<1/2,1

AB - In this paper, we prove that the local time L(t,x) of one-dimensional diffusion process exists except for a set of (2,n) zero capacity for all n≥1. Moreover, we also prove that L(t,x) as a function of x∈R quasi-everywhere belongs to Besov spaces Bp,1α for α<1/2,1

KW - 60H10

KW - 60J55

KW - Besov spaces

KW - Capacity

KW - Local times

KW - n -parameter Ornstein-Uhlenbeck process

UR - http://www.scopus.com/inward/record.url?scp=0042349762&partnerID=8YFLogxK

U2 - 10.1016/S0167-7152(01)00033-5

DO - 10.1016/S0167-7152(01)00033-5

M3 - Article

AN - SCOPUS:0042349762

SN - 0167-7152

VL - 54

SP - 161

EP - 169

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 2

ER -

On the quasi-everywhere regularity of the local time of one-dimensional diffusion process in Besov space

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this