The Annals of Probability

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• Neighboring clusters in Bernoulli percolation AI翻译
  作者：Timar, Adam
  作者单位：Indiana University System; Indiana University Bloomington
  摘要：We consider Bernoulli percolation on a locally finite quasi-transitive unimodular graph and prove that two infinite clusters cannot have infinitely many pairs of vertices at distance I from one another or, in other words, that such graphs exhibit cluster repulsion. This partially answers a question of Haggstrom, Peres and Schonmann.
• Percolation on nonunimodular transitive graphs AI翻译
  作者：Timar, Adam
  作者单位：Indiana University System; Indiana University Bloomington
  摘要：We extend some of the fundamental results about percolation on unimodular nonamenable graphs to nonunimodular graphs. We show that they cannot have infinitely many infinite clusters at critical Bernoulli percolation. In the case of heavy clusters, this result has already been established, but it also follows from one of our results. We give a general necessary condition for nonunimodular graphs to have a phase with infinitely many heavy clusters. We present an invariant spanning tree with p(c)...
• Central limit theorem for stationary linear processes AI翻译
  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.
• Traces of symmetric Markov processes and their characterizations AI翻译
  作者：Chen, Zhen-Qing; Fukushima, Masatoshi; Ying, Jiangang
  作者单位：University of Washington; University of Washington Seattle; Kansai University; Fudan University
  摘要：Time change is one of the most basic and very useful transformations for Markov processes. The time changed process can also be regarded as the trace of the original process on the support of the Revuz measure used in the time change. In this paper we give a complete characterization of time changed processes of an arbitrary symmetric Markov process, in terms of the Beurling-Deny decomposition of their associated Dirichlet forms and of Feller measures of the process. In particular, we determin...
• Kolmogorov equations in infinite dimensions:: Well-posedness and regularity of solutions, with applications to stochastic generalized Burgers equations AI翻译
  作者：Rockner, Michael; Sobol, Zeev
  作者单位：Purdue University System; Purdue University; Purdue University System; Purdue University; Swansea University
  摘要：We develop a new method to uniquely solve a large class of heat equations. so-called Kolmogorov equations in infinitely many variables. The equations are analyzed in spaces of sequentially weakly continuous functions weighted by proper (Lyapunov type) functions. This way for the first time the solutions are constructed everywhere without exceptional sets for equations with possibly nonlocally Lipschitz drifts. Apart from general analytic interest, the main motivation is to apply this to unique...
• An annihilating-branching particle model for the heat equation with average temperature zero AI翻译
  作者：Burdzy, Krzysztof; Quastel, Jeremy
  作者单位：University of Washington; University of Washington Seattle; University of Toronto
  摘要：We consider two species of particles performing random walks in a domain in R-d with reflecting boundary conditions, which annihilate on contact. In addition, there is a conservation law so that the total number of particles of each type is preserved: When the two particles of different species annihilate each other, particles of each species, chosen at random, give birth. We assume initially equal numbers of each species and show that the system has a diffusive scaling limit in which the dens...
• Feller processes on nonlocally compact spaces AI翻译
  作者：Szarek, Tomasz
  摘要：We consider Feller processes on a complete separable metric space X satisfying the ergodic condition of the form limsup n ->infinity (1/n Sigma P-n(i=1)i(x, 0)) > 0 for some x epsilon X, where O is an arbitrary open neighborhood of some point z epsilon X and P is a transition function. It is shown that e-chains which satisfy the above condition admit an invariant probability measure. Some results on the stability of such processes are also presented.
• A characterization of the infinitely divisible squared Gaussian processes AI翻译
  作者：Eisenbaum, Nathalie; Kaspi, Haya
  作者单位：Sorbonne Universite; Technion Israel Institute of Technology
  摘要：We show that, up to multiplication by constants, a Gaussian process has an infinitely divisible square if and only if its covariance is the Green function of a transient Markov process.
• Central limit theorems for additive functionals of the simple exclusion process (vol 34, pg 427, 2006) AI翻译
  作者：Sethuraman, S
  作者单位：Iowa State University
• A note about Khoshnevisan-Xiao conjecture AI翻译
  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 ...