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作者：Delmas, JF
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
摘要：We consider a super-Brownian motion X. Its canonical measures can be studied through the path-valued process called the Brownian snake. We obtain the limiting behavior of the volume of the epsilon-neighborhood for the range of the Brownian snake, and as a consequence we derive the analogous result for the range of super-Brownian motion and for the support of the integrated super-Brownian excursion. Then we prove the support of X-t is capacity-equivalent to [0, 1](2) in R-d, d greater than or e...
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作者：Colubi, A; López-Díaz, M; Domínguez-Menchero, JS; Gil, MA
作者单位：University of Oviedo
摘要：Strong laws of large numbers have been stated in the literature for measurable functions taking on values on different spaces. In this paper, a strong law of large numbers which generalizes some previous ones (like those for real-valued random variables and compact random sets) is established. This law is an example of a strong law of large numbers for Borel measurable nonseparably valued elements of a metric space.
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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 ...
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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 ...
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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...
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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 ...
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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.
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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?
