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On the occupation time of an iterated process having no local time

Author

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  • Csáki, Endre
  • Csörgo, Miklós
  • Földes, Antónia
  • Révész, Pál

Abstract

We study the asymptotic behaviour of the occupation time process [integral operator]t0 IA(W1(L2(s)))ds, t [greater-or-equal, slanted] 0, where W1 is a standard Wiener process and L2 is a Wiener local time process at zero that is independent from W1. We prove limit laws, as well as almost sure upper and lower class theorems. Possible extensions of the obtained results are also discussed.

Suggested Citation

  • Csáki, Endre & Csörgo, Miklós & Földes, Antónia & Révész, Pál, 1997. "On the occupation time of an iterated process having no local time," Stochastic Processes and their Applications, Elsevier, vol. 70(2), pages 199-217, October.
    • Handle: RePEc:eee:spapps:v:70:y:1997:i:2:p:199-217
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    References listed on IDEAS

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    1. Hu, Y. & Shi, Z., 1995. "The Csörgo-Révész modulus of non-differentiability of iterated Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 267-279, August.
    2. Shi, Z., 1995. "Lower limits of iterated Wiener processes," Statistics & Probability Letters, Elsevier, vol. 23(3), pages 259-270, May.
    3. Csáki, Endre & Csörgo, Miklós & Földes, Antónia & Révész, Pál, 1995. "Global Strassen-type theorems for iterated Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 59(2), pages 321-341, October.
    4. Bertoin, Jean, 1996. "Iterated Brownian motion and stable() subordinator," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 111-114, April.
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