Holder continuity and occupation-time formulas for fBm self-intersection local time and its derivative

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)

Abstract

We prove joint Holder continuity and an occupation-time formula for the self-intersection local time of fractional Brownian motion. Motivated by an occupation-time formula, we also introduce a new version of the derivative of self-intersection local time for fractional Brownian motion and prove Holder conditions for this process. This process is related to a different version of the derivative of self-intersection local time studied by the authors in a previous work.
Original languageEnglish
Pages (from-to)299-312
Number of pages14
JournalJournal of Theoretical Probability
Volume28
Issue number1
DOIs
Publication statusPublished - 2015

Keywords

  • Intersection local time
  • Fractional Brownian motion
  • Occupation-time formula

Cite this

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title = "Holder continuity and occupation-time formulas for fBm self-intersection local time and its derivative",
abstract = "We prove joint Holder continuity and an occupation-time formula for the self-intersection local time of fractional Brownian motion. Motivated by an occupation-time formula, we also introduce a new version of the derivative of self-intersection local time for fractional Brownian motion and prove Holder conditions for this process. This process is related to a different version of the derivative of self-intersection local time studied by the authors in a previous work.",
keywords = "Intersection local time, Fractional Brownian motion, Occupation-time formula",
author = "Paul Jung and Markowsky, {Gregory Tycho}",
year = "2015",
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language = "English",
volume = "28",
pages = "299--312",
journal = "Journal of Theoretical Probability",
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Holder continuity and occupation-time formulas for fBm self-intersection local time and its derivative. / Jung, Paul; Markowsky, Gregory Tycho.

In: Journal of Theoretical Probability, Vol. 28, No. 1, 2015, p. 299-312.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Holder continuity and occupation-time formulas for fBm self-intersection local time and its derivative

AU - Jung, Paul

AU - Markowsky, Gregory Tycho

PY - 2015

Y1 - 2015

N2 - We prove joint Holder continuity and an occupation-time formula for the self-intersection local time of fractional Brownian motion. Motivated by an occupation-time formula, we also introduce a new version of the derivative of self-intersection local time for fractional Brownian motion and prove Holder conditions for this process. This process is related to a different version of the derivative of self-intersection local time studied by the authors in a previous work.

AB - We prove joint Holder continuity and an occupation-time formula for the self-intersection local time of fractional Brownian motion. Motivated by an occupation-time formula, we also introduce a new version of the derivative of self-intersection local time for fractional Brownian motion and prove Holder conditions for this process. This process is related to a different version of the derivative of self-intersection local time studied by the authors in a previous work.

KW - Intersection local time

KW - Fractional Brownian motion

KW - Occupation-time formula

UR - http://link.springer.com/content/pdf/10.1007%2Fs10959-012-0474-8.pdf

U2 - 10.1007/s10959-012-0474-8

DO - 10.1007/s10959-012-0474-8

M3 - Article

VL - 28

SP - 299

EP - 312

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

SN - 0894-9840

IS - 1

ER -