![]() Döbler, Christian ![]() ![]() in Annals of Probability (in press) Detailed reference viewed: 435 (30 UL)![]() Campese, Simon ![]() ![]() in Annals of Probability (2020), 48(1), 147-177 Detailed reference viewed: 212 (9 UL)![]() Thalmaier, Anton ![]() ![]() in Annals of Probability (2019), 47(2), 743-773 Detailed reference viewed: 525 (110 UL)![]() ; Campese, Simon ![]() 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: 97 (2 UL)![]() ; Nourdin, Ivan ![]() in Annals of Probability (2018), 46(4), 2243-2267 Detailed reference viewed: 222 (6 UL)![]() Nourdin, Ivan ![]() ![]() in Annals of Probability (2016), 44(1), 1-41 Detailed reference viewed: 216 (12 UL)![]() 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: 153 (9 UL)![]() Azmoodeh, Ehsan ![]() in Annals of Probability (2015), 44 Detailed reference viewed: 120 (9 UL)![]() Nourdin, Ivan ![]() in Annals of Probability (2014), 42(2), 497-526 Detailed reference viewed: 116 (3 UL)![]() Nourdin, Ivan ![]() ![]() in Annals of Probability (2013), 41(4), 2709--2723 Detailed reference viewed: 173 (4 UL)![]() ; Nourdin, Ivan ![]() ![]() in Annals of Probability (2012), 40(4), 1577--1635 Detailed reference viewed: 198 (2 UL)![]() Peccati, Giovanni ![]() in Annals of Probability (2010), 38(2), 443--478 Detailed reference viewed: 163 (0 UL)![]() Nourdin, Ivan ![]() ![]() in Annals of Probability (2010), 38(5), 1947--1985 Detailed reference viewed: 170 (3 UL)![]() Nourdin, Ivan ![]() ![]() in Annals of Probability (2009), 37(4), 1412--1426 Detailed reference viewed: 193 (3 UL)![]() Nourdin, Ivan ![]() ![]() in Annals of Probability (2009), 37(6), 2231--2261 Detailed reference viewed: 193 (1 UL)![]() Nourdin, Ivan ![]() in Annals of Probability (2009), 37(6), 2200-2230 Detailed reference viewed: 93 (1 UL)![]() ![]() ; Peccati, Giovanni ![]() in Annals of Probability (2008), 36(6), 2280--2310 Detailed reference viewed: 145 (0 UL)![]() Nourdin, Ivan ![]() in Annals of Probability (2008), 36(6), 2159-2175 Detailed reference viewed: 49 (3 UL)![]() ; Nourdin, Ivan ![]() in Annals of Probability (2007), 35(5), 1998-2020 Detailed reference viewed: 101 (7 UL)![]() ![]() Peccati, Giovanni ![]() in Annals of Probability (2006), 34(3), 1217--1239 Detailed reference viewed: 95 (0 UL) |
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