Jean-Christophe Breton

Exact confidence intervals for the Hurst parameter of a fractional Brownian motion

In this short note, we show how to use concentration inequal- ities in order to build exact confidence intervals for the Hurst parameter associated with a one-dimensional fractional Brownian motion. AMS 2000 subject classifications: Primary 60G15; secondary 60F05,

Rescaled weighted random ball models and stable self-similar random fields

We consider weighted random balls in distributed according to a random Poisson measure with heavy-tailed intensity and study the asymptotic behavior of the total weight of some configurations in while we perform a zooming operation. The resulting procedure is very rich and several regimes appear in the limit, depending on the intensity of the balls, the zooming factor, the tail parameters of the radii and the weights. Statistical properties of the limit fields are also evidenced, such as isotropy, self-similarity or dependence. One regime is of particular interest and yields [alpha]-stable stationary isotropic self-similar generalized random fields which recovers Takenaka fields, Telecom process or fractional Brownian motion.

Asymptotics for random Young diagrams when the word length and alphabet size simultaneously grow to infinity

Given a random word of size

Multiple Stable Stochastic Integrals: Series Representation and Absolute Continuity of Their Law

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Intégrales stables multiples : représentation, absolue continuité de leur loi

whose letters are drawn independently from an ordered alphabet of size

Convex comparison inequalities for non-Markovian stochastic integrals

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On the limiting law of the length of the longest common and increasing subsequences in random words

, the fluctuations of the shape of the random RSK Young tableaux are investigated, when

Bounds on Option Prices in Point Process Diffusion Models

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Principe local d'invariance pour des variables aléatoires i.i.d.

and

Contact angle and surface tension of water on a hexagonal boron nitride monolayer: a methodological investigation

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