Processes iterated ad libitum

Jérôme Casse and Jean-François Marckert

Stochastic Processes and their Applications, 2016, vol. 126, issue 11, 3353-3376

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.

Keywords: Iterated Brownian motion; Exchangeability; Weak convergence; Stable processes (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:126:y:2016:i:11:p:3353-3376

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DOI: 10.1016/j.spa.2016.04.031

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