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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...
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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...
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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 ...
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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...
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作者：Bie, ESL
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Clermont Auvergne (UCA)
摘要：We study a Stochastic Partial Differential Equation, of parabolic type, set on IRd, with d is an element of N. This equation is driven by a Poisson random measure, either compensated or not. The first part of this work shows existence and uniqueness of a progressively measurable solution. The technics involved are close to those used to deal with analogous equations driven by a Gaussian noise. The second part gives some criterions on the intensity of the Poisson random measure, in order to ens...
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作者：Zahle, M
作者单位：Friedrich Schiller University of Jena
摘要：The classical Lebesgue-Stieltjes integral integral(a)(b)f dg of real or complex-valued functions on a finite interval (a, b) is extended to a large class of integrands f and integrators g of unbounded variation. The key is to use composition formulas and integration-by-part rules for fractional integrals and Weyl derivatives. In the special case of Holder continuous functions f and g of summed order greater than 1 convergence of the corresponding Riemann-Stieltjes sums is proved. The results a...
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作者：Sun, YE
作者单位：National University of Singapore; Yale University
摘要：For a large collection of random variables in an ideal setting, pairwise independence is shown to be almost equivalent to mutual independence. An asymptotic interpretation of this fact shows the equivalence of asymptotic pairwise independence and asymptotic mutual independence for a triangular array (or a sequence) of random variables. Similar equivalence is also presented for uncorrelatedness and orthogonality as well as for the constancy of joint moment functions and exchangeability. General...
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作者：Benjamini, I; Schramm, O
作者单位：Weizmann Institute of Science
摘要：Consider the standard continuous percolation in IR4, and choose the parameters so that the induced percolation on a fixed two dimensional linear subspace is critical. Although two dimensional critical percolation dies, we show that there are exceptional two dimensional linear subspaces, in which percolation occurs.
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作者：Toth, B; Werner, W
作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Hungarian Academy of Sciences; Universite Paris Saclay
摘要：We construct and study a continuous real-valued random process, which is of a new type: It is self-interacting (self-repelling) but only in a local sense: it only feels the self-repellance due to its occupation-time measure density in the 'immediate neighbourhood' of the point it is just visiting. We focus on the most natural process with these properties that we call 'true self-repelling motion'. This is the continuous counterpart to the integer-valued 'true' self-avoiding walk, which had bee...
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作者：Toubol, A
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite Paris Cite
摘要：Comets and Neveu have initiated in [5] a method to prove convergence of the partition function of disordered systems to a lognormal random variable in the high temperature regime by means of stochastic calculus. We generalize their approach to a multidimensional Sherrington-Kirkpatrick model with an application to the Heisenberg model of uniform spins on a sphere of R-d, see [9]. The main tool that we use is a truncation of the partition function outside a small neighbourhood of the typical en...
