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作者：Nourdin, Ivan; Peccati, Giovanni
作者单位：Sorbonne Universite; Universite Paris Cite; Universite Paris Nanterre; Universite Paris Saclay
摘要：We show how to detect optimal Berry-Esseen bounds in the normal approximation of functionals of Gaussian fields. Our techniques are based on a combination of Malliavin calculus, Stein's method and the method of moments and cumulants, and provide de facto local (one-term) Edgeworth expansions. The findings of the present paper represent a further refinement of the main results proven in Nourdin and Peccati [Probab. Theory Related Fields 145 (2009) 75-118]. Among several examples, we discuss thr...
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作者：Tudor, Ciprian A.; Viens, Frederi G.
作者单位：heSam Universite; Universite Pantheon-Sorbonne; Purdue University System; Purdue University; Purdue University System; Purdue University
摘要：Using multiple stochastic integrals and the Malliavin calculus, we analyze the asymptotic behavior of quadratic variations for a specific non-Gaussian self-similar process, the Rosenblatt process. We apply our results to the design of strongly consistent statistical estimators for the self-similarity parameter H. Although, in the case of the Rosenblatt process, our estimator has non-Gaussian asymptotics for all H > 1/2, we show the remarkable fact that the process's data at time 1 can be used ...
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作者：Duquesne, Thomas
作者单位：Sorbonne Universite; Universite Paris Cite
摘要：We prove that the total range of Super-Brownian motion with quadratic branching mechanism has an exact packing measure with respect to the gauge function g(r) = r(4)(log log l/r)(-3) in super-critical dimensions d >= 5. More precisely, we prove that the total occupation measure of Super-Brownian motion is equal to the g-packing measure restricted to its range, up to a deterministic multiplicative constant that only depends on space dimension d.
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作者：Chatterjee, Shirshendu; Durrett, Rick
作者单位：Cornell University
摘要：If we consider the contact process with infection rate lambda on a random graph on n vertices with power law degree distributions, mean field calculations suggest that the critical value lambda(c) of the infection rate is positive if the power alpha > 3. Physicists seem to regard this as an established fact, since the result has recently been generalized to bipartite graphs by Gomez-Gardefies et al. [Proc. Nad. Acad. Sci. USA 105 (2008) 1399-1404]. Here, we show that the critical value lambda(...
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作者：Spakulova, Iva
作者单位：Vanderbilt University
摘要：This article presents a method for finding the critical probability pc for the Bernoulli bond percolation on graphs with the so-called tree-like structure. Such a graph can be decomposed into a tree of pieces, each of which has finitely many isomorphism classes. This class of graphs includes the Cayley graphs of amalgamated products, HNN extensions or general groups acting on trees. It also includes all transitive graphs with more than one end. The idea of the method is to find a multi-type Ga...
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作者：Bentkus, Vidmantas; Jing, Bing-Yi; Zhou, Wang
作者单位：Vilnius University; Hong Kong University of Science & Technology; National University of Singapore
摘要：Let X-1, ..., X-n be i.i.d. random observations. Let S = L + T be a U-statistic of order k >= 2 where L is a linear statistic having asymptotic normal distribution, and T is a stochastically smaller statistic. We show that the rate of convergence to normality for S can be simply expressed as the rate of convergence to normality for the linear part L plus a correction term, (varT) ln(2) (varT), under the condition ET2 < infinity. An optimal bound without this log factor is obtained under a lowe...
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作者：Hochman, Michael
作者单位：Hebrew University of Jerusalem
摘要：For arrays (S(i, j))(1 <= i <= j) of random variables that are stationary in an appropriate sense, we show that the fluctuations of the process (S(l, n))(n=1)(infinity) can be bounded in terms of a measure of the mean subadditivity of the process (S(i, j))(1 <= i <= j). We derive universal upcrossing inequalities with exponential decay for Kingman's subadditive ergodic theorem, the Shannon-MacMillan-Breiman theorem and for the convergence of the Kolmogorov complexity of a stationary sample.
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作者：Reinert, Gesine; Roellin, Adrian
作者单位：University of Oxford; National University of Singapore
摘要：In this paper we establish a multivariate exchangeable pairs approach within the framework of Stein's method to assess distributional distances to potentially singular multivariate normal distributions. By extending the statistics into a higher-dimensional space, we also propose an embedding method which allows for a normal approximation even when the corresponding statistics of interest do not lend themselves easily to Stein's exchangeable pairs approach. To illustrate the method, we provide ...
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作者：Hu, Yaozhong; Nualart, David; Song, Jian
作者单位：University of Kansas
摘要：In this paper we introduce the notion of fractional martingale as the fractional derivative of order a of a continuous local martingale, where alpha is an element of (-1/2, 1/2) and we show that it has a nonzero finite variation of order 2/1+2 alpha, under some integrability assumptions on the quadratic variation of the local martingale. As an application we establish an extension of Levy's characterization theorem for the fractional Brownian motion.
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作者：Rasonyi, Miklos; Schachermayer, Walter; Warnung, Richard
作者单位：Hungarian Academy of Sciences; HUN-REN; HUN-REN Institute for Computer Science & Control; University of Vienna
摘要：In this article we consider a Brownian motion with drift of the form dS(t) = mu(t)dt + dB(t) for t >= 0, with a specific nontrivial (mu(t))(t) >= 0, predictable with respect to F-B, the natural filtration of the Brownian motion B = (B-t)(t >= 0). We construct a process H = (H-t)(t >= 0), also predictable with respect to F-B such that ((H center dot S)(t))(t >= 0) is a Brownian motion in its own filtration. Furthermore, for any delta > 0, we refine this construction such that the drift (mu(t))(...
