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作者：Berestycki, Julien; Berestycki, Nathanael; Schweinsberg, Jason
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; University of Cambridge; University of California System; University of California San Diego
摘要：We consider a system of particles which perform branching Brownian motion with negative drift and are killed upon reaching zero, in the near-critical regime where the total population stays roughly constant with approximately N particles. We show that the characteristic time scale for the evolution of this population is of order (log N)(3), in the sense that when time is measured in these units, the scaled number of particles converges to a variant of Neveu's continuous-state branching process...
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作者：Crawford, Nicholas; Sly, Allan
作者单位：Technion Israel Institute of Technology; University of California System; University of California Berkeley
摘要：We study limit laws for simple random walks on supercritical long-range percolation clusters on Z(d), d >= 1. For the long range percolation model, the probability that two vertices x, y are connected behaves asymptotically as parallel to x - y parallel to(-s)(2). When s is an element of (d, d + 1), we prove that the scaling limit of simple random walk on the infinite component converges to an a-stable Levy process with alpha = s - d establishing a conjecture of Berger and Biskup [Probab. Theo...
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作者：Bednorz, Witold
作者单位：University of Warsaw
摘要：In this paper we prove the complete characterization of a.s. convergence of orthogonal series in terms of existence of a majorizing measure. It means that for a given (a(n))(n=1)(infinity), a(n) > 0, series Sigma(infinity)(n=1) a(n)phi(n) is a.e. convergent for each orthonormal sequence (phi(n))(n=1)(infinity) if and only if there exists a measure m on T = {0} boolean OR {Sigma(m)(n=1) a(n)(2), m >= 1} such that sup(t is an element of T)integral(root D(T))(0) (m(B(t, r(2))))(-1/2) dr < infinit...
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作者：Gurel-Gurevich, Ori; Nachmias, Asaf
作者单位：University of British Columbia
摘要：We show that the distribution of the first return time tau to the origin, v, of a simple random walk on an infinite recurrent graph is heavy tailed and nonconcentrated. More precisely, if d(v) is the degree of v, then for any t >= 1 we have P-v(tau >= t) >= c/d(v)root t and P-v(tau = t vertical bar tau >= t) <= C log(d(v)t)/t for some universal constants c > 0 and C < infinity. The first bound is attained for all t when the underlying graph is Z, and as for the second bound, we construct an ex...
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作者：Marcus, Michael B.; Rosen, Jay
作者单位：City University of New York (CUNY) System; City College of New York (CUNY); City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：We provide a sufficient condition for the continuity of real valued permanental processes. When applied to the subclass of permanental processes which consists of squares of Gaussian processes, we obtain the sufficient condition for continuity which is also known to be necessary. Using an isomorphism theorem of Eisenbaum and Kaspi which relates Markov local times and permanental processes, we obtain a general sufficient condition for the joint continuity of local times.
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作者：Biskamp, Moritz
作者单位：Technical University of Berlin
摘要：It has been shown by various authors that the diameter of a given nontrivial bounded connected set X grows linearly in time under the action of an isotropic Brownian flow (IBF), which has a nonnegative top-Lyapunov exponent. In case of a planar IBF with a positive top-Lyapunov exponent, the precise deterministic linear growth rate K of the diameter is known to exist. In this paper we will extend this result to an asymptotic support theorem for the time-scaled trajectories of a planar IBF phi, ...
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作者：Pal, Soumik
作者单位：University of Washington; University of Washington Seattle
摘要：We study a family of n-dimensional diffusions, taking values in the unit simplex of vectors with nonnegative coordinates that add up to one. These processes satisfy stochastic differential equations which are similar to the ones for the classical Wright-Fisher diffusions, except that the mutation rates are now nonpositive. This model, suggested by Aldous, appears in the study of a conjectured diffusion limit for a Markov chain on Cladograms. The striking feature of these models is that the bou...
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作者：Xiong, Jie
作者单位：University of Tennessee System; University of Tennessee Knoxville; University of Macau
摘要：A stochastic partial differential equation (SPDE) is derived for super-Brownian motion regarded as a distribution function valued process. The strong uniqueness for the solution to this SPDE is obtained by an extended Yamada-Watanabe argument. Similar results are also proved for the Fleming-Viot process.
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作者：Hazra, Rajat Subhra; Maulik, Krishanu
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：In this article, we introduce the notion of free subexponentiality, which extends the notion of subexponentiality in the classical probability setup to the noncommutative probability spaces under freeness. We show that distributions with regularly varying tails belong to the class of free subexponential distributions. This also shows that the partial sums of free random elements having distributions with regularly varying tails are tail equivalent to their maximum in the sense of Ben Arous and...
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作者：Merlevede, Florence; Peligrad, Magda
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); University System of Ohio; University of Cincinnati
摘要：The aim of this paper is to propose new Rosenthal-type inequalities for moments of order higher than 2 of the maximum of partial sums of stationary sequences including martingales and their generalizations. As in the recent results by Peligrad et al. [Proc. Amer. Math. Soc. 135 (2007) 541-550] and Rio [J. Theoret. Probab. 22 (2009) 146-163], the estimates of the moments are expressed in terms of the norms of projections of partial sums. The proofs of the results are essentially based on a new ...
