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作者：Latala, Rafal
作者单位：University of Warsaw
摘要：We derive two-sided estimates on moments and tails of Gaussian chaoses, that is, random variables of the form Sigma a(i1),...,i(d)g(i1) center dot center dot center dot g(id), where g(i) are i.i.d. N(0, 1) r.v.s. Estimates are exact up to constants depending on d only.
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作者：Rossignol, Raphael
作者单位：Universite Paris Cite
摘要：Threshold phenomena are investigated using a general approach, following Talagrand [Ann. Probab. 22 (1994) 1576-1587] and Friedgut and Kalai [Proc. Amer. Math. Soc. 12 (1999) 1017-1054]. The general upper bound for the threshold width of symmetric monotone properties is improved. This follows from a new lower bound on the maximal influence of a variable on a Boolean function. The method of proof is based on a well-know n logarithmic Sobolev inequality on {0, 1}(n). This new bound is shown to b...
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作者：Goldys, B.; Maslowski, B.
作者单位：University of New South Wales Sydney; Czech Academy of Sciences; Institute of Mathematics of the Czech Academy of Sciences
摘要：A formula for the transition density of a Markov process defined by an infinite-dimensional stochastic equation is given in terms of the Ornstein-Uhlenbeck bridge and a useful lower estimate on the density is provided. As a consequence, uniform exponential ergodicity and V-ergodicity are proved for a large class of equations. We also provide computable bounds on the convergence rates and the spectral gap for the Markov semigroups defined by the equations. The bounds turn out to be uniform with...
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作者：Bramson, Maury; Zeitouni, Ofer; Zerner, Martin P. W.
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Technion Israel Institute of Technology; Technion Israel Institute of Technology; Eberhard Karls University of Tubingen; Stanford University; University of California System; University of California Davis
摘要：We construct forests that span Z(d), d >= 2, that are stationary and directed, and whose trees are infinite, but for which the subtrees attached to each vertex are as short as possible. For d >= 3, two independent copies of such forests, pointing in opposite directions, can be pruned so as to become disjoint. From this, we construct in d >= 3 a stationary, polynomially mixing and uniformly elliptic environment of nearest-neighbor transition probabilities on Z(d) for which the corresponding ran...
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作者：Dawson, D. A.; Li, Zenghu
作者单位：Carleton University; Beijing Normal University
摘要：A general affine Markov semigroup is formulated as the convolution of a homogeneous one with a skew convolution semigroup. We provide some sufficient conditions for the regularities of the homogeneous affine semigroup and the skew convolution semigroup. The corresponding affine Markov process is constructed as the strong solution of a system of stochastic equations with non-Lipschitz coefficients and Poisson-type integrals over some random sets. Based on this characterization, it is proved tha...
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作者：Gnedin, Alexander; Pitman, Jim; Yor, Marc
作者单位：Utrecht University; Sorbonne Universite; University of California System; University of California Berkeley
摘要：A random composition of n appears when the points of a random closed set (R) over tilde subset of [0, 1] are used to separate into blocks n points sampled from the uniform distribution. We study the number of parts K-n of this composition and other related functionals under the assumption that (R) over tilde = phi(S-center dot), where (S-t, t >= 0) is a subordinator and phi:[0, infinity] -> [0, 1] is a diffeomorphism. We derive the asymptotics of K-n when the Levy measure of the subordinator i...
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作者：Kaise, H; Sheu, SJ
作者单位：Nagoya University; Academia Sinica - Taiwan
摘要：Bellman equations of ergodic type related to risk-sensitive control are considered. We treat the case that the nonlinear term is positive quadratic form on first-order partial derivatives of solution, which includes linear exponential quadratic Gaussian control problem. In this paper we prove that the equation in general has multiple solutions. We shall specify the set of all the classical solutions and classify the solutions by a global behavior of the diffusion process associated with the gi...
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作者：Bressaud, X.; Maass, A.; Martinez, S.; San Martin, J.
作者单位：Aix-Marseille Universite; Universidad de Chile
摘要：We study the standard property of the natural filtration associated to a 0-1 valued stationary process. In our main result we show that if the process has summable memory decay, then the associated filtration is standard. We prove it by coupling techniques. For a process whose associated filtration is standard, we construct a product type filtration extending it, based upon the usual couplings and the Vershik's criterion for standardness.
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作者：Brossard, Jean; Leuridan, Christophe
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
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作者：Peccati, Giovanni; Thieullen, Michele; Tudor, Ciprian A.
作者单位：Sorbonne Universite; Sorbonne Universite; Universite Paris Cite
摘要：Let the process {Y-t, t is an element of [0, 1]} have the form Y-t = delta(u1([o,t])), where delta stands for a Skorohod integral with respect to Brownian motion and u is a measurable process that verifies some suitable regularity conditions. We use a recent result by Tudor to prove that Y-t can be represented as the limit of linear combinations of processes that are products of forward and backward Brownian martingales. Such a result is a further step toward the connection between the theory ...
