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The purpose of this note is to prove a central limit theorem for the third integrated moment of the Brownian local time increments using techniques of stochastic analysis.. This
Key words: Central limit theorem, excited random walk, law of large numbers, positive and negative cookies, recurrence, renewal structure, transience.. AMS 2000 Subject
Amongst other things, Aldous proved that the CRT is the scaling limit of a wide class of discrete random trees (in particular it is the scaling limit of uniformly distributed
It follows from our Theorem 2.1 that the limit results proved for heights and (or) lengths of excursions for the case of Brownian motion remain valid for similar quantities of
The main result of this paper is the following local limit theorem for the joint distribution of the vector ( |C1| ,. , |C k | ) in the Erd˝ os-Rényi random graph:.. Theorem 1.1
Keywords: Total variation distance; Non-central limit theorem; Fractional Brownian motion; Hermite power variation; Multiple stochastic integrals; Hermite random
It was proved in (7) that SLE(2) is the scaling limit of the corresponding loop-erased random walk (LERW), and SLE(8) is the scaling limit of some uniform spanning tree (UST)
But by the central limit theorem for m-dependent stationary sequence (see for example Brockwell and Davis, 1990, page 213), the latter is asymptotically normal with mean zero
