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On the logarithmic average of iterated processes

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  • Csáki, Endre
  • Földes, Antónia

Abstract

We prove almost sure convergence for the logarithmic average of f(W(X(t))/[psi](t)), where f is a suitable function, [psi](t) is a norming factor, W is a Wiener process and X is a suitable process, independent of W. Particular attention is paid for the case when X is the local time of a Wiener process or a reflected Wiener process.

Suggested Citation

  • Csáki, Endre & Földes, Antónia, 1997. "On the logarithmic average of iterated processes," Statistics & Probability Letters, Elsevier, vol. 33(4), pages 347-358, May.
    • Handle: RePEc:eee:stapro:v:33:y:1997:i:4:p:347-358
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    References listed on IDEAS

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    1. Shi, Z., 1995. "Lower limits of iterated Wiener processes," Statistics & Probability Letters, Elsevier, vol. 23(3), pages 259-270, May.
    2. Lacey, Michael T. & Philipp, Walter, 1990. "A note on the almost sure central limit theorem," Statistics & Probability Letters, Elsevier, vol. 9(3), pages 201-205, March.
    3. Marcus, Michael B. & Rosen, Jay, 1995. "Logarithmic averages for the local times of recurrent random walks and Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 59(2), pages 175-184, October.
    4. Horvath, Lajos & Khoshnevisan, Davar, 1995. "Weight functions and pathwise local central limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 59(1), pages 105-123, September.
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