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Processes iterated ad libitum

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  • Casse, Jérôme
  • Marckert, Jean-François

Abstract

Consider the nth iterated Brownian motion I(n)=Bn∘⋯∘B1. Curien and Konstantopoulos proved that for any distinct numbers ti≠0, (I(n)(t1),…,I(n)(tk)) converges in distribution to a limit I[k] independent of the ti’s, exchangeable, and gave some elements on the limit occupation measure of I(n). Here, we prove under some conditions, finite dimensional distributions of nth iterated two-sided stable processes converge, and the same holds the reflected Brownian motions. We give a description of the law of I[k], of the finite dimensional distributions of I(n), as well as those of the iterated reflected Brownian motion iterated ad libitum.

Suggested Citation

  • Casse, Jérôme & Marckert, Jean-François, 2016. "Processes iterated ad libitum," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3353-3376.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:11:p:3353-3376
    DOI: 10.1016/j.spa.2016.04.031
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    References listed on IDEAS

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    1. Bertoin, Jean, 1996. "Iterated Brownian motion and stable() subordinator," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 111-114, April.
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    Cited by:

    1. Chen, Zhe & Leskelä, Lasse & Viitasaari, Lauri, 2019. "Pathwise Stieltjes integrals of discontinuously evaluated stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2723-2757.

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