作者：Devroye, Luc; Lugosi, Gabor
作者单位：McGill University; Pompeu Fabra University; ICREA; Pompeu Fabra University
摘要：It is shown that functions defined on {0, 1,..., r - 1}(n) satisfying certain conditions of bounded differences that guarantee sub-Gaussian tail behavior also satisfy a much stronger local sub-Gaussian property. For self-bounding and configuration functions we derive analogous locally subexponential behavior. The key tool is Talagrand's [Ann. Probab. 22 (1994) 1576-1587] variance inequality for functions defined on the binary hypercube which we extend to functions of uniformly distributed rand...
作者：Singh, Arvind
作者单位：Sorbonne Universite
摘要：We consider a diffusion process X in a random Levy potential V which is a solution of the informal stochastic differential equation {dX(t) = d beta(t)-1/2V '(X-t)dt, X-0 = 0, (beta B. M. independent of V). We study the rate of convergence when the diffusion is transient under the assumption that the Levy process V does not possess positive jumps. We generalize the previous results of Hu-Shi-Yor for drifted Brownian potentials. In particular, we prove a conjecture of Carmona: provided that ther...
