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作者：Adler, Robert J.; Samorodnitsky, Gennady; Taylor, Jonathan E.
作者单位：Technion Israel Institute of Technology; Cornell University; Stanford University
摘要：We consider smooth, infinitely divisible random fields (X (t), t is an element of M), M subset of R-d, with regularly varying Levy measure, and are interested in the geometric characteristics of the excursion sets A(u) = {t is an element of M : X(t) > u} over high levels u. For a large class of such random fields, we compute the u -> infinity asymptotic joint distribution of the numbers of critical points, of various types, of X in A(u), conditional on A(u) being nonempty. This allows us, for ...
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作者：Chen, Louis H. Y.; Fang, Xiao; Shao, Qi-Man
作者单位：National University of Singapore; National University of Singapore; Hong Kong University of Science & Technology; Chinese University of Hong Kong
摘要：Stein's method is applied to obtain a general Cramer-type moderate deviation result for dependent random variables whose dependence is defined in terms of a Stein identity. A corollary for zero-bias coupling is deduced. The result is also applied to a combinatorial central limit theorem, a general system of binary codes, the anti-voter model on a complete graph, and the Curie-Weiss model. A general moderate deviation result for independent random variables is also proved.
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作者：Kallenberg, Olav
作者单位：Auburn University System; Auburn University
摘要：Consider a locally finite Dawson-Watanabe superprocess xi = (xi(t)) in R-d with d >= 2. Our main results include some recursive formulas for the moment measures of xi, with connections to the uniform Brownian tree, a Brownian snake representation of Palm measures, continuity properties of conditional moment densities, leading by duality to strongly continuous versions of the multivariate Palm distributions, and a local approximation of xi(t) by a stationary cluster (eta) over tilde with nice c...
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作者：Angel, Omer; Goodman, Jesse; Merle, Mathieu
作者单位：University of British Columbia; Leiden University - Excl LUMC; Leiden University; Universite Paris Cite
摘要：We prove existence of the scaling limit of the invasion percolation cluster (IPC) on a regular tree. The limit is a random real tree with a single end. The contour and height functions of the limit are described as certain diffusive stochastic processes. This convergence allows us to recover and make precise certain asymptotic results for the MC. In particular, we relate the limit of the rescaled level sets of the MC to the local time of the scaled height function.
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作者：Inahama, Yuzuru
作者单位：Nagoya University
摘要：We consider a rough differential equation indexed by a small parameter epsilon > 0. When the rough differential equation is driven by fractional Brownian motion with Hurst parameter H (1/4 < H < 1/2), we prove the Laplace-type asymptotics for the solution as the parameter 8 tends to zero.
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作者：Dereich, Steffen; Moerters, Peter
作者单位：University of Munster; University of Bath
摘要：We study a dynamical random network model in which at every construction step a new vertex is introduced and attached to every existing vertex independently with a probability proportional to a concave function f of its current degree. We give a criterion for the existence of a giant component, which is both necessary and sufficient, and which becomes explicit when f is linear. Otherwise it allows the derivation of explicit necessary and sufficient conditions, which are often fairly close. We ...
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作者：Mossel, Elchanan; Sly, Allan
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：We establish tight results for rapid mixing of Gibbs samplers for the Ferromagnetic Ising model on general graphs. We show that if (d - 1) tanh beta < 1, then there exists a constant C such that the discrete time mixing time of Gibbs samplers for the ferromagnetic Ising model on any graph of n vertices and maximal degree d, where all interactions are bounded by beta, and arbitrary external fields are bounded by Cn log n. Moreover, the spectral gap is uniformly bounded away from 0 for all such ...
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作者：Wang, Yizao; Roy, Parthanil; Stoev, Stilian A.
作者单位：University of Michigan System; University of Michigan; Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：We establish characterization results for the ergodicity of stationary symmetric alpha-stable (S alpha S) and alpha-Frechet random fields. We show that the result of Samorodnitsky [Ann. Probab. 33 (2005) 1782-1803] remains valid in the multiparameter setting, that is, a stationary S alpha S (0 < alpha < 2) random field is ergodic (or, equivalently, weakly mixing) if and only if it is generated by a null group action. Similar results are also established for max-stable random fields. The key in...
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作者：Calka, Pierre; Schreiber, Tomasz; Yukich, J. E.
作者单位：Universite de Rouen Normandie; Nicolaus Copernicus University; Lehigh University
摘要：Schreiber and Yukich [Ann. Probab. 36 (2008) 363-396] establish an asymptotic representation for random convex polytope geometry in the unit ball B-d, d >= 2, in terms of the general theory of stabilizing functionals of Poisson point processes as well as in terms of generalized paraboloid growth processes. This paper further exploits this connection, introducing also a dual object termed the paraboloid hull process. Via these growth processes we establish local functional limit theorems for th...
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作者：Cont, Rama; Fournie, David-Antoine
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Columbia University
摘要：We develop a nonanticipative calculus for functionals of a continuous semimartingale, using an extension of the Ito formula to path-dependent functionals which possess certain directional derivatives. The construction is based on a pathwise derivative, introduced by Dupire, for functionals on the space of right-continuous functions with left limits. We show that this functional derivative admits a suitable extension to the space of square-integrable martingales. This extension defines a weak d...
