-
作者：Barron, A; Birgé, L; Massart, P
作者单位：Yale University; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
摘要：Performance bounds for criteria for model selection are developed using recent theory for sieves. The model selection criteria are based on an empirical loss or contrast function with an added penalty term motivated by empirical process theory and roughly proportional to the number of parameters needed to describe the model divided by the number of observations. Most of our examples involve density or regression estimation settings and we focus on the problem of estimating the unknown density ...
-
作者：Fontes, LRG; Isopi, M; Newman, CM
作者单位：Universidade de Sao Paulo; Sapienza University Rome; New York University
摘要：Stochastic Ising and voter models on Z(d) are natural examples of Markov processes with compact state spaces. When the initial state is chosen uniformly at random, can it happen that the distribution at time t has multiple (subsequence) limits as t --> infinity? Yes for the d = 1 Voter Model with Random Rates (VMRR)- which is the same as a d = 1 rate-disordered stochastic Ising model at zero temperature - if the disorder distribution is heavy-tailed. No (at least in a weak sense) for the VMRR ...
-
作者：Barral, J
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：Here, a Mandelbrot measure is a statistically self-similar measure mu on the boundary of a c-ary tree, obtained by multiplying random weights indexed by the nodes of the tree. We take a particular interest in the random variable Y = parallel to mu parallel to : we study the existence of finite moments of negative orders for Y, conditionally to Y > 0, and the continuity properties of Y with respect to the weights. Our results on moments make possible to study, with probability one, the existenc...
-
作者：Chow, PL; Ibragimov, IA; Khasminskii, RZ
作者单位：Wayne State University; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences
摘要：For linear partial differential equations, some inverse source problems are treated statistically based on nonparametric estimation ideas. By observing the solution in a small Gaussian white noise, the kernel type of estimators is used to estimate the unknown source function and its partial derivatives.. It is proved that such estimators are consistent as the noise intensity tends to zero. Depending on the principal part of the differential operator, the optimal asymptotic rate of convergence ...
-
作者：Bertoin, J
作者单位：Sorbonne Universite
摘要：We investigate the nature of the intersection of two independent regenerative sets. The approach combines Bochner's subordination and potential theory for a pair of Markov processes in duality.
-
作者：Wu, LM
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Clermont Auvergne (UCA)
摘要：Let L := Delta/2 + (del phi/phi) . del be a generalized Schrodinger operator or generator of Nelson's diffusion, defined on C-0(infinity)(D) where phi is a continuous and strictly positive function on an open domain D subset of R-d such that del phi is an element of L-loc(2)(D). Some results are given about the two questions below: (i) Whether does L generate a unique semigroup in L-1(D, phi(2) dx)? (ii) Whether the semigroup determined by L is strong Feller?
-
作者：Chueshov, ID; Vuillermot, PA
作者单位：Ministry of Education & Science of Ukraine; VN Karazin Kharkiv National University; Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS)
摘要：In this article we prove new results concerning the long-time behavior of random fields that are solutions in some sense to a class of semilinear parabolic equations subjected to a homogeneous and multiplicative white noise. Our main results state that these random fields eventually homogeneize with respect to the spatial variable and finally converge to a non-random global attractor which consists of two spatially and temporally homogeneous asymptotic states. More precisely, we prove that the...
-
作者：Giraitis, L; Taqqu, MS; Terrin, N
作者单位：Vilnius University; Boston University; Tufts Medical Center
摘要：Let (X-t, t is an element of Z) be a linear sequence with non-Gaussian innovations and a spectral density which varies regularly at low frequencies. This includes situations, known as strong (or long-range) dependence, where the spectral density diverges at the origin. We study quadratic forms of bivariate Appell polynomials of the sequence (X-t) and provide general conditions for these quadratic forms, adequately normalized, to converge to a non-Gaussian distribution, We consider, in particul...
-
作者：Schilling, RL
作者单位：Nottingham Trent University; Universite Paris Saclay
摘要：Let (A,D(A)) be the infinitesimal generator of a Feller semigroup such that C-c(infinity)(R-n) subset of D(A) and A\C-c(infinity)(R-n) is a pseudo-differential operator with symbol -p(x,xi) satisfying parallel to p(.,xi parallel to(infinity) less than or equal to c(1 + parallel to xi parallel to(2)) and \Im p(x,xi)\ less than or equal to c(0) Re p(x,xi). We show that the associated Feller process {X-t}(t greater than or equal to 0) on R-n is a semimartingale, even a homogeneous diffusion with ...
-
作者：Talagrand, M
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); University System of Ohio; Ohio State University
摘要：Consider 0 < alpha < 1 and the Gaussian process Y(t) on R-N with covariance E(Y(s)Y(t)) = \t\(2 alpha) + \s\(2 alpha) - \t - s\(2 alpha), where \t\ is the Euclidean norm of t. Consider independent copies X-1,...,X-d of Y and the process X(t) = (X-1(t),...,X-d(t)) valued in R-d. When kN less than or equal to (k - 1)alpha d, we show that the trajectories of X do not have k-multiple points. If N < alpha d and kN > (k - 1)alpha d, the set of k-multiple points of the trajectories X is a countable u...
