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LAMN property for hidden processes : the case of integrated diffusions

Arnaud Gloter, Emmanuel Gobet (2008)

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

In this paper we prove the Local Asymptotic Mixed Normality (LAMN) property for the statistical model given by the observation of local means of a diffusion process X. Our data are given by ∫01X(s+i)/n dμ(s) for i=0, …, n−1 and the unknown parameter appears in the diffusion coefficient of the process X only. Although the data are neither markovian nor gaussian we can write down, with help of Malliavin calculus, an explicit expression for the log-likelihood of the model, and then study the asymptotic...

Limit Theorems for Non-Critical Branching Processes with Continuous State Space

Kurbanov, S. (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary 60J80, Secondary 60G99.In the paper a modification of the branching stochastic process with immigration and with continuous states introduced by Adke S. R. and Gadag V. G. (1995) is considered. Limit theorems for the non-critical processes with or without non-stationary immigration and finite variance are proved. The subcritical case is illustrated with examples.

Limiting curlicue measures for theta sums

Francesco Cellarosi (2011)

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

We consider the ensemble of curves {γα, N: α∈(0, 1], N∈ℕ} obtained by linearly interpolating the values of the normalized theta sum N−1/2∑n=0N'−1exp(πin2α), 0≤N'<N. We prove the existence of limiting finite-dimensional distributions for such curves as N→∞, when α is distributed according to any probability measure λ, absolutely continuous w.r.t. the Lebesgue measure on [0, 1]. Our Main Theorem generalizes a result by Marklof [Duke Math. J.97 (1999) 127–153] and Jurkat and van Horne [Duke...

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