-
作者：Cassandro, Marzio; Orlandi, Enza; Picco, Pierre
作者单位：Consiglio Nazionale delle Ricerche (CNR); Istituto Nazionale per la Fisica della Materia (INFM-CNR); Sapienza University Rome; Roma Tre University; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：Estimate (3.39) which appears in the proof of Proposition 3.4 in [Ann. Probab. 27 (1999) 1414-1467] is wrong. We present below a corrected proof which introduces an extra factor 2 in equations (3.34) and (3.35). This has no consequence in the rest of the paper since Proposition 3.4 is used to estimate only ratios; see (3.23) and (3.25).
-
作者：Kratz, Marie F.; Leon, Jose R.
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; University of Central Venezuela
摘要：Cramer and Leadbetter introduced in 1967 the sufficient condition r(s)-r(0)/s is an element of L-1([0,delta], dx), delta > 0, to have a finite variance of the number of zeros of a centered stationary Gaussian process with twice differentiable covariance function r. This condition is known as the Geman condition, since Geman proved in 1972 that it was also a necessary condition. Up to now no such criterion was known for counts of crossings of a level other than the mean, This paper shows that t...
-
作者：Asselah, Amine; Ferrari, Pablo A.
作者单位：Aix-Marseille Universite; Universidade de Sao Paulo
摘要：We consider a system of asymmetric independent random walks on Z(d), denoted by {eta(t), t is an element of R}, stationary under the product Poisson measure v(rho) of marginal density p > 0. We fix a pattern A, an increasing local event, and denote by tau the hitting time of A. By using a loss network representation of our system, at small density, we obtain a coupling between the laws of eta(t) conditioned on (tau > t) for all times t. When d >= 3, this provides bounds on the rate of converge...
-
作者：Jiang, Tiefeng
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We solve an open problem of Diaconis that asks what are the largest orders of p(n) and q(n) such that Z(n), the p(n) x q(n) upper left block of a random matrix Gamma(n) which is uniformly distributed on the orthogonal group O(n), can be approximated by independent standard normals? This problem is solved by two different approximation methods. First, we show that the variation distance between the joint distribution of entries of Z(n) and that of p(n)q(n) independent standard normals goes to z...
-
作者：Dalang, Robert C.; Mueller, C.; Zambotti, L.
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of Rochester; Polytechnic University of Milan
摘要：We study the hitting properties of the solutions u of a class of parabolic stochastic partial differential equations with singular drifts that prevent u from becoming negative. The drifts can be a reflecting term or a nonlinearity cu(-3), with c > 0. We prove that almost surely, for all time t > 0, the solution ut hits the level 0 only at a finite number of space points, which depends explicitly on c. In particular, this number of hits never exceeds 4 and if c > 15/8, then level 0 is not hit.
-
作者：Hoffman, Christopher; Holroyd, Alexander E.; Peres, Yuval
作者单位：University of Washington; University of Washington Seattle; University of British Columbia; University of California System; University of California Berkeley
摘要：Let Xi be a discrete set in R-d. Call the elements of Xi centers. The well-known Voronoi tessellation partitions R-d into polyhedral regions (of varying sizes) by allocating each site of R-d to the closest center. Here we study fair allocations of R-d to Iota in which the regions allocated to different centers have equal volumes. We prove that if Xi is obtained from a translation-invariant point process, then there is a unique fair allocation which is stable in the sense of the Gale-Shapley ma...
-
作者：Bahadoran, C.; Guiol, H.; Ravishankar, K.; Saada, E.
作者单位：Universite Clermont Auvergne (UCA); State University of New York (SUNY) System; University at Albany, SUNY; SUNY New Paltz; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider attractive irreducible conservative particle systems on Z, without necessarily nearest-neighbor jumps or explicit invariant measures. We prove that for such systems, the hydrodynamic limit under Enter time scaling exists and is given by the entropy solution to some scalar conservation law with Lipschitz-continuous flux. Our approach is a generalization of Bahadoran et al. [Stochastic Process. Appl. 99 (2002) 1-30], from which we relax the assumption that the process has explicit in...
-
作者：Peligrad, Magda; Utev, Sergey
作者单位：University System of Ohio; University of Cincinnati; University of Nottingham
摘要：We establish the central limit theorem for linear processes with dependent innovations including martingales and mixingale type of assumptions as defined in McLeish [Ann. Probab. 5 (1977) 616-621] and motivated by Gordin [Soviet Math. Dokl. 10 (1969) 1174-1176]. In doing so we shall preserve the generality of the coefficients, including the long range dependence case, and we shall express the variance of partial sums in a form easy to apply. Ergodicity is not required.
-
作者：Manstavicius, Martynas
作者单位：University of Connecticut
摘要：Khoshnevisan and Xiao showed in [Ann. Probab. 33 (2005) 841-878] that the statement about almost surely vanishing Bessel-Riesz capacity of the image of a Borel set G subset of R+ under a symmetric Levy process X in R-d is equivalent to the vanishing of a deterministic f-capacity for a particular function f defined in terms of the characteristic exponent of X. The authors conjectured that a similar statement is true for all Levy processes in R-d. We show that the conjecture is true provided we ...
-
作者：Gallardo, Leonard; Yor, Marc
作者单位：Universite de Tours; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
摘要：Dunkl processes are martingales as well as cadlag homogeneous Markov processes taking values in R-d and they are naturally associated with a root system. In this paper we study the jumps of these processes, we describe precisely their martingale decompositions into continuous and purely discontinuous parts and we obtain a Wiener chaos decomposition of the corresponding L-2 spaces of these processes in terms of adequate mixed multiple stochastic integrals.
