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Showing 2013 · math.PRShow all

13 papers · 2 filters

math.PR2013★ 62 cited

The scaling limit of uniform random plane maps, via the Ambjørn-Budd bijection

Jérémie Bettinelli, Emmanuel Jacob, Grégory Miermont

We prove that a uniform rooted plane map with n edges converges in distribution after a suitable normalization to the Brownian map for the Gromov-Hausdorff topology. A recent bijec…

math.PR2013

An Itô's type formula for the fractional Brownian motion in Brownian time

Ivan Nourdin, Raghid Zeineddine

Let be a (two-sided) fractional Brownian motion of Hurst parameter and let be a standard Brownian motion independent of . Fractional Brownian motion in Brow…

math.PR2013★ 3 cited

Cross-variation of Young integral with respect to long-memory fractional Brownian motions

Ivan Nourdin, Rola Zintout

We study the asymptotic behaviour of the cross-variation of two-dimensional processes having the form of a Young integral with respect to a fractional Brownian motion of index $H \…

math.PR2013★ 13 cited

Information Transmission under Random Emission Constraints

Francis Comets, François Delarue, René Schott

We model the transmission of a message on the complete graph with n vertices and limited resources. The vertices of the graph represent servers that may broadcast the message at ra…

math.PR2013★ 1 cited

Comparison inequalities on Wiener space

Ivan Nourdin, Giovanni Peccati, Frederi Viens

We define a covariance-type operator on Wiener space: for F and G two random variables in the Gross-Sobolev space of random variables with a square-integrable Malliavin d…

math.PR2013

Convergence in law implies convergence in total variation for polynomials in independent Gaussian, Gamma or Beta random variables

Ivan Nourdin, Guillaume Poly

Consider a sequence of polynomials of bounded degree evaluated in independent Gaussian, Gamma or Beta random variables. We show that, if this sequence converges in law to a noncons…

math.PR2013★ 2 cited

The optimal fourth moment theorem

Ivan Nourdin, Giovanni Peccati

We compute the exact rates of convergence in total variation associated with the 'fourth moment theorem' by Nualart and Peccati (2005), stating that a sequence of random variables…

math.PR2013★ 28 cited

Quantitative stable limit theorems on the Wiener space

Ivan Nourdin, David Nualart, Giovanni Peccati

We use Malliavin operators in order to prove quantitative stable limit theorems on the Wiener space, where the target distribution is given by a possibly multidimensional mixture o…

math.PR2013

On L2 modulus of continuity of Brownian local times and Riesz potentials

Aurélien Deya, David Nualart, Samy Tindel

This article is concerned with modulus of continuity of Brownian local times. Specifically, we focus on 3 closely related problems: (a) Limit theorem for a Brownian modulus of cont…

math.PR2013

Strong solutions to stochastic differential equations with rough coefficients

Nicolas Champagnat, Pierre-Emmanuel Jabin

We study strong existence and pathwise uniqueness for stochastic differential equations in $\RR^d$ with rough coefficients, and without assuming uniform ellipticity for the diffusi…

math.PR2013★ 1 cited

Adaptation in a stochastic multi-resources chemostat model

Nicolas Champagnat, Pierre-Emmanuel Jabin, Sylvie Méléard

We are interested in modeling the Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions, in the specific sc…

math.PR2013★ 16 cited

On the rough-paths approach to non-commutative stochastic calculus

Aurélien Deya, René Schott

We study different possibilities to apply the principles of rough paths theory in a non-commutative probability setting. First, we extend previous results obtained by Capitaine, Do…

math.PR2013

Asymptotic behavior of mixed power variations and statistical estimation in mixed models

Marco Dozzi, Yuliya Mishura, Georgiy Shevchenko

We obtain results on both weak and almost sure asymptotic behaviour of power variations of a linear combination of independent Wiener process and fractional Brownian motion. These…