Local Time and Local Reflection of the Wiener Process

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Abstract

In this paper we introduce a concept of a Brownian trajectory local reflection. Ideologically, this concept is close to the concept of the Brownian local time, which can be considered as the integrated (over time) Dirac delta function of a Brownian trajectory. In the concept of the local reflection, we replace the Dirac delta function by its first derivative.

Original languageEnglish
Title of host publicationOperator Theory and Harmonic Analysis, OTHA 2020
EditorsAlexey N. Karapetyants, Igor V. Pavlov, Albert N. Shiryaev
PublisherSpringer Nature
Pages233-242
Number of pages10
ISBN (Print)9783030768287
DOIs
StatePublished - 2021
EventInternational Scientific Conference on Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis, OTHA 2020 - Rostov-on-Don, Russian Federation
Duration: 26 Apr 202030 Apr 2020

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume358
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational Scientific Conference on Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis, OTHA 2020
Country/TerritoryRussian Federation
CityRostov-on-Don
Period26/04/2030/04/20

Scopus subject areas

  • Mathematics(all)

Keywords

  • Limit theorem
  • Local time
  • Wiener process

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