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作者：Wang, Feng-Yu
作者单位：Beijing Normal University; Swansea University
摘要：Let P(t) be the diffusion semigroup generated by L := Delta + del V on a complete connected Riemannian manifold with Ric >= -(sigma(2)rho(2)(0) + c) for some constants sigma, c > 0 and rho(0) the Riemannian distance to a fixed point. It is shown that Pt is hypercontractive, or the log-Sobolev inequality holds for the associated Dirichlet form, provided - Hess(V) >= delta holds outside of a compact set for some constant delta > (1 +root 2)sigma root d-1. This indicates, at least in finite dimen...
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作者：Buckdahn, Rainer; Djehiche, Boualem; Li, Juan; Peng, Shige
作者单位：Universite de Bretagne Occidentale; Royal Institute of Technology; Shandong University; Shandong University
摘要：Mathematical mean-field approaches play an important role in different fields of Physics and Chemistry, but have found in recent works also their application in Economics, Finance and Game Theory. The objective of our paper is to investigate a special mean-field problem in a purely stochastic approach: for the solution (Y, Z) of a mean-field backward stochastic differential equation driven by a forward stochastic differential of McKean-Vlasov type with solution X we study a special approximati...
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作者：Nourdin, Ivan; Peccati, Giovanni
作者单位：Universite Paris Cite; Sorbonne Universite; Universite Paris Nanterre; Sorbonne Universite
摘要：Fix nu > 0, denote by G(nu/2) a Gamma random variable with parameter nu/2 and let n >= 2 be a fixed even integer. Consider a sequence {F-k}(k >= 1) of square integrable random variables belonging to the nth Wiener chaos of a given Gaussian process and with valiance converging to 2 nu. As k -> infinity, we prove that F-k converges in distribution to 2G(nu/2) - nu if and only if E(F-k(4)) - 12E(F-k(3)) -> 12 nu(2) - 48 nu.
