Displaying similar documents to “Asymptotic behavior of the Empirical Process for Gaussian data presenting seasonal long-memory”

A generalized mean-reverting equation and applications

Nicolas Marie (2014)

ESAIM: Probability and Statistics

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Consider a mean-reverting equation, generalized in the sense it is driven by a 1-dimensional centered Gaussian process with Hölder continuous paths on [0] (> 0). Taking that equation in rough paths sense only gives local existence of the solution because the non-explosion condition is not satisfied in general. Under natural assumptions, by using specific methods, we show the global existence and uniqueness of the solution, its integrability, the continuity and differentiability...

Nonparametric inference for discretely sampled Lévy processes

Shota Gugushvili (2012)

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

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Given a sample from a discretely observed Lévy process = ( )≥0 of the finite jump activity, the problem of nonparametric estimation of the Lévy density corresponding to the process is studied. An estimator of is proposed that is based on a suitable inversion of the Lévy–Khintchine formula and a plug-in device. The main results of the paper deal with upper risk bounds for estimation of over suitable classes of Lévy triplets. The corresponding lower bounds are also...

Local asymptotic normality for normal inverse gaussian Lévy processes with high-frequency sampling

Reiichiro Kawai, Hiroki Masuda (2013)

ESAIM: Probability and Statistics

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We prove the local asymptotic normality for the full parameters of the normal inverse Gaussian Lévy process , when we observe high-frequency data , ,, with sampling mesh  → 0 and the terminal sampling time  → ∞. The rate of convergence turns out to be (√, √, √, √) for the dominating parameter (), where stands for the heaviness of the tails, the degree of skewness, the scale, and the location. The essential feature in...

Simulation and approximation of Lévy-driven stochastic differential equations

Nicolas Fournier (2011)

ESAIM: Probability and Statistics

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We consider the approximate Euler scheme for Lévy-driven stochastic differential equations. We study the rate of convergence in law of the paths. We show that when approximating the small jumps by Gaussian variables, the convergence is much faster than when simply neglecting them. For example, when the Lévy measure of the driving process behaves like ||d near , for some ∈ (1,2), we obtain an error of order 1/√ with a computational cost of order . For a similar error when neglecting...

Survival probabilities of autoregressive processes

Christoph Baumgarten (2014)

ESAIM: Probability and Statistics

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Given an autoregressive process of order (  =   + ··· +   +  where the random variables , ,... are i.i.d.), we study the asymptotic behaviour of the probability that the process does not exceed a constant barrier up to time (survival or persistence probability). Depending on the coefficients ,...,...