The asymptotic behaviour of local times and occupation integrals of the N-parameter Wiener process in Rd

Peter Imkeller, F. Weisz

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

Let L(x, T), x∈Rd, T∈R+N, be the local time of the N-parameter Wiener process W taking values in Rd. Even in the distribution valued cased d≧2 N, L can be described in a series representation by means of multiple Wiener-Ito integrals. This setting proves to be a good starting point for the investigation of the asymptotic behaviour of L(x, T) as |x|→0 and/or T∞ and of related occupation integrals {Mathematical expression} as T→∞. We obtain the rates of explosion in laws of the first order, i.e. normalized convergence laws for L(x, T) resp. XT(f), and of the second order, i.e. normalized convergence laws for L(x, T)-E(L(x, T)) resp. XT(f)-E(XT(f)).

Original languageEnglish
Pages (from-to)47-75
Number of pages29
JournalProbability Theory and Related Fields
Volume98
Issue number1
DOIs
Publication statusPublished - Mar 1994

Fingerprint

Wiener Process
Local Time
Asymptotic Behavior
Itô Integral
Wiener Integral
Series Representation
Explosion
First-order
Local time
Wiener process
Asymptotic behavior
Integral

Keywords

  • Mathematics Subject Classification (1990): 60G60, 60J55, 60G15, 60H05

ASJC Scopus subject areas

  • Statistics and Probability
  • Analysis
  • Mathematics(all)

Cite this

The asymptotic behaviour of local times and occupation integrals of the N-parameter Wiener process in Rd. / Imkeller, Peter; Weisz, F.

In: Probability Theory and Related Fields, Vol. 98, No. 1, 03.1994, p. 47-75.

Research output: Contribution to journalArticle

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