Continuous Breuer-Major theorem: tightness and non-stationarity

in Annals of Probability (2020), 48(1), 147-177

Four Moments Theorems on Markov Chaos

in Annals of Probability (2019), 47(3), 1417-1446

We obtain quantitative four moments theorems establishing convergence of the laws of elements of a Markov chaos to a Pearson distribution, where the only assumption we make on the Pearson distribution is ... [more ▼]

We obtain quantitative four moments theorems establishing convergence of the laws of elements of a Markov chaos to a Pearson distribution, where the only assumption we make on the Pearson distribution is that it admits four moments. These results are obtained by first proving a general carré du champ bound on the distance between laws of random variables in the domain of a Markov diffusion generator and invariant measures of diffusions, which is of independent interest, and making use of the new concept of chaos grade. For the heavy-tailed Pearson distributions, this seems to be the first time that sufficient conditions in terms of (finitely many) moments are given in order to converge to a distribution that is not characterized by its moments. [less ▲]

Weak symmetric integrals with respect to the fractional Brownian motion

in Annals of Probability (2018), 46(4), 2243-2267

Discrete versions of the transport equation and the Shepp-Olkin conjecture

in Annals of Probability (2016), 44(1), 276-306

We introduce a framework to consider transport problems for integer-valued random variables. We introduce weighting coeffcients which allow us to characterise transport problems in a gradient now setting ... [more ▼]

We introduce a framework to consider transport problems for integer-valued random variables. We introduce weighting coeffcients which allow us to characterise transport problems in a gradient now setting, and form the basis of our introduction of a discrete version of the Benamou--Brenier formula. Further, we use these coeffcients to state a new form of weighted log-concavity. These results are applied to prove the monotone case of the Shepp--Olkin entropy concavity conjecture. [less ▲]

Asymptotic independence of multiple Wiener-Itô integrals and the resulting limit laws

in Annals of Probability (2014), 42(2), 497-526

Wigner chaos and the fourth moment

in Annals of Probability (2012), 40(4), 1577--1635

Stein's method and normal approximation of Poisson functionals

in Annals of Probability (2010), 38(2), 443--478

Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: the critical case H=1/4

in Annals of Probability (2009), 37(6), 2200-2230

Hoeffding decompositions and urn sequences

in Annals of Probability (2008), 36(6), 2280--2310

Stochastic derivatives for fractional diffusions

in Annals of Probability (2007), 35(5), 1998-2020