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The fourth moment theorem on the Poisson space Döbler, Christian ; Peccati, Giovanni in Annals of Probability (in press) Detailed reference viewed: 373 (30 UL)Continuous Breuer-Major theorem: tightness and non-stationarity Campese, Simon ; Nourdin, Ivan ; in Annals of Probability (2020), 48(1), 147-177 Detailed reference viewed: 183 (9 UL)Derivative and divergence formulae for diffusion semigroups Thalmaier, Anton ; Thompson, James in Annals of Probability (2019), 47(2), 743-773 Detailed reference viewed: 468 (107 UL)Four Moments Theorems on Markov Chaos ; Campese, Simon ; et al 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 ▲] Detailed reference viewed: 75 (2 UL)Weak symmetric integrals with respect to the fractional Brownian motion ; Nourdin, Ivan ; in Annals of Probability (2018), 46(4), 2243-2267 Detailed reference viewed: 203 (5 UL)Quantitative stable limit theorems on the Wiener space Nourdin, Ivan ; ; Peccati, Giovanni in Annals of Probability (2016), 44(1), 1-41 Detailed reference viewed: 193 (12 UL)Discrete versions of the transport equation and the Shepp-Olkin conjecture Hillion, Erwan ; 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 ▲] Detailed reference viewed: 136 (9 UL)Generalization of the Nualart-Peccati criterion Azmoodeh, Ehsan ; ; et al in Annals of Probability (2015), 44 Detailed reference viewed: 100 (9 UL)Asymptotic independence of multiple Wiener-Itô integrals and the resulting limit laws Nourdin, Ivan ; in Annals of Probability (2014), 42(2), 497-526 Detailed reference viewed: 100 (3 UL)Poisson approximations on the free Wigner chaos Nourdin, Ivan ; Peccati, Giovanni in Annals of Probability (2013), 41(4), 2709--2723 Detailed reference viewed: 148 (4 UL)Wigner chaos and the fourth moment ; Nourdin, Ivan ; Peccati, Giovanni et al in Annals of Probability (2012), 40(4), 1577--1635 Detailed reference viewed: 178 (2 UL)Stein's method and normal approximation of Poisson functionals Peccati, Giovanni ; ; et al in Annals of Probability (2010), 38(2), 443--478 Detailed reference viewed: 145 (0 UL)Invariance principles for homogeneous sums: universality of Gaussian Wiener chaos Nourdin, Ivan ; Peccati, Giovanni ; in Annals of Probability (2010), 38(5), 1947--1985 Detailed reference viewed: 151 (3 UL)Noncentral convergence of multiple integrals Nourdin, Ivan ; Peccati, Giovanni in Annals of Probability (2009), 37(4), 1412--1426 Detailed reference viewed: 169 (3 UL)Stein's method and exact Berry-Esseen asymptotics for functionals of Gaussian fields Nourdin, Ivan ; Peccati, Giovanni in Annals of Probability (2009), 37(6), 2231--2261 Detailed reference viewed: 168 (1 UL)Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: the critical case H=1/4 Nourdin, Ivan ; in Annals of Probability (2009), 37(6), 2200-2230 Detailed reference viewed: 78 (1 UL)Hoeffding decompositions and urn sequences ; Peccati, Giovanni in Annals of Probability (2008), 36(6), 2280--2310 Detailed reference viewed: 125 (0 UL)Asymptotic behavior of certain weighted quadratic and cubic variations of fractional Brownian motion Nourdin, Ivan in Annals of Probability (2008), 36(6), 2159-2175 Detailed reference viewed: 33 (3 UL)Stochastic derivatives for fractional diffusions ; Nourdin, Ivan in Annals of Probability (2007), 35(5), 1998-2020 Detailed reference viewed: 84 (7 UL)Martingale structure of Skorohod integral processes Peccati, Giovanni ; ; in Annals of Probability (2006), 34(3), 1217--1239 Detailed reference viewed: 72 (0 UL) |
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