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Iterating Brownian motions, ad libitum
Let B1, B2, ... be independent one-dimensional Brownian motions defined over the whole real line such that Bi(0) = 0 for every i ≥ 1. We consider the nth iterated Brownian motion Wn(t) = Bn(Bn−1(...(B2(B1(t)))...)). Although the sequences of processes (Wn)n≥1 do not converge in a functional sense, we prove that the finite-dimensional marginals converge. As a consequence, we deduce that the rand...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2016
ISSN: 0304-4149
DOI: 10.1016/j.spa.2016.04.031