Displaying similar documents to “Sharp estimates for the convergence of the density of the Euler scheme in small time.”

The rate of convergence for spectra of GUE and LUE matrix ensembles

Friedrich Götze, Alexander Tikhomirov (2005)

Open Mathematics

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We obtain optimal bounds of order O(n −1) for the rate of convergence to the semicircle law and to the Marchenko-Pastur law for the expected spectral distribution functions of random matrices from the GUE and LUE, respectively.

Euler scheme for SDEs with non-Lipschitz diffusion coefficient : strong convergence

Abdel Berkaoui, Mireille Bossy, Awa Diop (2008)

ESAIM: Probability and Statistics

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We consider one-dimensional stochastic differential equations in the particular case of diffusion coefficient functions of the form | x | α , α ∈ [ 1 / 2 , 1 ) . In that case, we study the rate of convergence of a symmetrized version of the Euler scheme. This symmetrized version is easy to simulate on a computer. We prove its strong convergence and obtain the same rate of convergence as when the coefficients are Lipschitz.

Intermittency properties in a hyperbolic Anderson problem

Robert C. Dalang, Carl Mueller (2009)

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

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We study the asymptotics of the even moments of solutions to a stochastic wave equation in spatial dimension 3 with linear multiplicative spatially homogeneous gaussian noise that is white in time. Our main theorem states that these moments grow more quickly than one might expect. This phenomenon is well known for parabolic stochastic partial differential equations, under the name of intermittency. Our results seem to be the first example of this phenomenon for hyperbolic equations....