Displaying similar documents to “A generalized mean-reverting equation and applications”

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...

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...

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 ,...,...

Universality of slow decorrelation in KPZ growth

Ivan Corwin, Patrik L. Ferrari, Sandrine Péché (2012)

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

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There has been much success in describing the limiting spatial fluctuations of growth models in the Kardar–Parisi–Zhang (KPZ) universality class. A proper rescaling of time should introduce a non-trivial temporal dimension to these limiting fluctuations. In one-dimension, the KPZ class has the dynamical scaling exponent = 3/2, that means one should find a universal space–time limiting process under the scaling of time as , space like 2/3 and fluctuations like 1/3 as → ∞. In this paper...

Means in complete manifolds: uniqueness and approximation

Marc Arnaudon, Laurent Miclo (2014)

ESAIM: Probability and Statistics

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Let be a complete Riemannian manifold,  ∈ ℕ and  ≥ 1. We prove that almost everywhere on  = ( ,, ) ∈  for Lebesgue measure in , the measure μ ( x ) = N ∑ k = 1 N x k μ ( x ) = 1 N ∑ k = 1 N δ x k has a unique–mean (). As a consequence, if  = ( ,, ) is a -valued random variable with absolutely continuous law, then almost surely (()) has a unique –mean. In particular if ( ...

Hydrodynamic limit of a d-dimensional exclusion process with conductances

Fábio Júlio Valentim (2012)

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

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Fix a polynomial of the form () = + ∑2≤≤    =1 with (1) gt; 0. We prove that the evolution, on the diffusive scale, of the empirical density of exclusion processes on 𝕋 d , with conductances given by special class of functions, is described by the unique weak solution of the non-linear parabolic partial differential equation = ∑    ...

Universality in the bulk of the spectrum for complex sample covariance matrices

Sandrine Péché (2012)

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

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We consider complex sample covariance matrices = (1/)* where is a × random matrix with i.i.d. entries , 1 ≤ ≤ , 1 ≤ ≤ , with distribution . Under some regularity and decay assumptions on , we prove universality of some local eigenvalue statistics in the bulk of the spectrum in the limit where → ∞ and lim→∞ / = for any real number ∈ (0, ∞).

Variational approximation of a functional of Mumford–Shah type in codimension higher than one

Francesco Ghiraldin (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we consider a new kind of Mumford–Shah functional () for maps : ℝ → ℝ with  ≥ . The most important novelty is that the energy features a singular set of codimension greater than one, defined through the theory of distributional jacobians. After recalling the basic definitions and some well established results, we prove an approximation property for the energy ()  −convergence, in the same spirit of the work by Ambrosio and Tortorelli [L....

Model selection and estimation of a component in additive regression

Xavier Gendre (2014)

ESAIM: Probability and Statistics

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Let  ∈ ℝ be a random vector with mean and covariance matrix where is some known  × -matrix. We construct a statistical procedure to estimate as well as under moment condition on or Gaussian hypothesis. Both cases are developed for known or unknown . Our approach is free from any prior assumption on and is based on non-asymptotic model selection methods....

Linear diffusion with stationary switching regime

Xavier Guyon, Serge Iovleff, Jian-Feng Yao (2010)

ESAIM: Probability and Statistics

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Let be a Ornstein–Uhlenbeck diffusion governed by a stationary and ergodic process : ddd. We establish that under the condition with the stationary distribution of the regime process , the diffusion is ergodic. We also consider conditions for the existence of moments for the invariant law of when is a Markov jump process having a finite number of states. Using results on random difference equations on one hand and the fact that conditionally to , is Gaussian on the other...

Discrete sampling of an integrated diffusion process and parameter estimation of the diffusion coefficient

Arnaud Gloter (2010)

ESAIM: Probability and Statistics

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Let () be a diffusion on the interval and a sequence of positive numbers tending to zero. We define as the integral between and of . We give an approximation of the law of by means of a Euler scheme expansion for the process (). In some special cases, an approximation by an explicit Gaussian ARMA(1,1) process is obtained. When we deduce from this expansion estimators of the diffusion coefficient of based on (). These estimators are shown to...