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Cerf, Raphaël Dembin, Barbara

We consider the anchored isoperimetric profile of the infinite open cluster, defined for p > p_c, whose existence has been recently proved in [3]. We extend adequately the definition for p = p_c, in finite boxes. We prove a partial result which implies that, if the limit defining the anchored isoperimetric profile at pc exists, it has to vanish.

Lagnoux, Agnès

Lagnoux, Agnes Mercier, Sabine Vallois, Pierre

We calculate the probability density function of the local score position on complete excursions of a reflected Brownian motion. We use the trajecto-rial decomposition of the standard Brownian bridge to derive two different expressions of the density: the first one is based on a series and an integral while the second one is free off the series.

Chabriac, Claudie Lagnoux, Agnès Mercier, Sabine Vallois, Pierre

Elements related to the largest complete excursion of a reflected BM stopped at a fixed time. Application to local score.

Liechty, Karl
Published in
Journal of Statistical Physics

We study the distribution of the maximal height of the outermost path in the model of N nonintersecting Brownian motions on the half-line as N→∞, showing that it converges in the proper scaling to the Tracy-Widom distribution for the largest eigenvalue of the Gaussian orthogonal ensemble. This is as expected from the viewpoint that the maximal heig...

Labart, Céline Lelong, Jérôme

In this article, we study a double barrier version of the standard Parisian options. We give closed formulas for the Laplace transforms of their prices with respect to the maturity time. We explain how to invert them numerically and prove a result on the accuracy of the numerical inversion when the function to be recovered is sufficiently smooth. H...

Picard, Jean

A stochastic calculus similar to Malliavin's calculus is worked out for Brownian excursions. The analogue of the Malliavin derivative in this calculus is not a differential operator, but its adjoint is (like the Skorohod integral) an extension of the Itô integral. As an application, we obtain an expression for the integrand in the stochastic integr...