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Global Strassen-type theorems for iterated Brownian motions

Author

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

Abstract

A class of iterated processes is studied by proving a joint functional limit theorem for a pair of independent Brownian motions. This Strassen method is applied to prove global (t --> [infinity]), as well as local (t --> 0), LIL type results for various iterated processes. Similar results are also proved for iterated random walks via invariance.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:59:y:1995:i:2:p:321-341
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    Citations

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    Cited by:

    1. Liu, Jin V., 2013. "On Chung’s law of the iterated logarithm for the Brownian time Lévy’s area process," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1404-1410.
    2. 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.
    3. Gajda, Janusz & Magdziarz, Marcin, 2014. "Large deviations for subordinated Brownian motion and applications," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 149-156.
    4. Nane, Erkan, 2009. "Laws of the iterated logarithm for a class of iterated processes," Statistics & Probability Letters, Elsevier, vol. 79(16), pages 1744-1751, August.

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