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Strong approximations of additive functionals of a planar Brownian motion

Author

Listed:
  • Csáki, Endre
  • Földes, Antónia
  • Hu, Yueyun

Abstract

This paper is devoted to the study of the additive functional , 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 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.

Suggested Citation

  • Csáki, Endre & Földes, Antónia & Hu, Yueyun, 2004. "Strong approximations of additive functionals of a planar Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 109(2), pages 263-293, February.
    • Handle: RePEc:eee:spapps:v:109:y:2004:i:2:p:263-293
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    Cited by:

    1. Löcherbach, Eva & Loukianova, Dasha, 2009. "The law of iterated logarithm for additive functionals and martingale additive functionals of Harris recurrent Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2312-2335, July.

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