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A Poisson bridge between fractional Brownian motion and stable Lévy motion

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  • Gaigalas, Raimundas

Abstract

We study a non-Gaussian and non-stable process arising as the limit of sums of rescaled renewal processes under the condition of intermediate growth. The process has been characterized earlier by the cumulant generating function of its finite-dimensional distributions. Here, we derive a more tractable representation for it as a stochastic integral of a deterministic function with respect to a compensated Poisson random measure. Employing the representation we show that the process is locally and globally asymptotically self-similar with fractional Brownian motion and stable Lévy motion as its tangent limits.

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  • Gaigalas, Raimundas, 2006. "A Poisson bridge between fractional Brownian motion and stable Lévy motion," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 447-462, March.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:3:p:447-462
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    References listed on IDEAS

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    1. Cioczek-Georges, R. & Mandelbrot, B. B., 1996. "Alternative micropulses and fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 64(2), pages 143-152, November.
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    Cited by:

    1. Puplinskaitė, Donata & Surgailis, Donatas, 2015. "Scaling transition for long-range dependent Gaussian random fields," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2256-2271.
    2. Pilipauskaitė, Vytautė & Surgailis, Donatas, 2015. "Joint aggregation of random-coefficient AR(1) processes with common innovations," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 73-82.
    3. Pilipauskaitė, Vytautė & Surgailis, Donatas, 2014. "Joint temporal and contemporaneous aggregation of random-coefficient AR(1) processes," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 1011-1035.

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