Displaying similar documents to “On the central limit theorem for random variables related to the continued fraction expansion”

Planar Lorentz process in a random scenery

Françoise Pène (2009)

Annales de l'I.H.P. Probabilités et statistiques

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We consider the periodic planar Lorentz process with convex obstacles (and with finite horizon). In this model, a point particle moves freely with elastic reflection at the fixed convex obstacles. The random scenery is given by a sequence of independent, identically distributed, centered random variables with finite and non-null variance. To each obstacle, we associate one of these random variables. We suppose that each time the particle hits an obstacle, it wins the amount given by...

Limiting curlicue measures for theta sums

Francesco Cellarosi (2011)

Annales de l'I.H.P. Probabilités et statistiques

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We consider the ensemble of curves { , : ∈(0, 1], ∈ℕ} obtained by linearly interpolating the values of the normalized theta sum −1/2∑=0−1exp(πi2), 0≤<. We prove the existence of limiting finite-dimensional distributions for such curves as →∞, when is distributed according to any probability measure , absolutely continuous w.r.t. the Lebesgue measure on [0, 1]. Our Main Theorem generalizes a result by Marklof [ (1999) 127–153] and Jurkat and van...