Strong approximations of additive functionals of a planar Brownian motion

E. Csáki, Antónia Földes, Yueyun Hu

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper is devoted to the study of the additive functional t→ ∫0 t f(W(s)) ds, where f denotes a measurable function and W is a planar Brownian motion. Kasahara and Kotani (Z. Wahrsch. Verw. Gebiete 49(2) (1979) 133) have obtained its second-order asymptotic behavior, by using the skew-product representation of W and the ergodicity of the angular part. We prove that the vector (∫0 · fj(W(s)) ds1≤j≤n can be strongly approximated by a multi-dimensional Brownian motion time changed by an independent inhomogeneous Lévy process. This strong approximation yields central limit theorems and almost sure behaviors for additive functionals. We also give their applications to winding numbers and to symmetric Cauchy process.

Original languageEnglish
Pages (from-to)263-293
Number of pages31
JournalStochastic Processes and their Applications
Volume109
Issue number2
DOIs
Publication statusPublished - Feb 2004

Fingerprint

Additive Functionals
Strong Approximation
Brownian movement
Brownian motion
Second-order Asymptotics
Additive Functional
Winding number
Skew Product
Measurable function
Ergodicity
Central limit theorem
Cauchy
Asymptotic Behavior
Denote
Approximation
Asymptotic behavior

Keywords

  • Additive functionals
  • Strong approximation

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Mathematics(all)
  • Statistics and Probability

Cite this

Strong approximations of additive functionals of a planar Brownian motion. / Csáki, E.; Földes, Antónia; Hu, Yueyun.

In: Stochastic Processes and their Applications, Vol. 109, No. 2, 02.2004, p. 263-293.

Research output: Contribution to journalArticle

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