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作者：Pinsky, Ross G.
作者单位：Technion Israel Institute of Technology
摘要：Let the random variable Z(n,k) denote the number of increasing subsequences of length k in a random permutation from S-n, the symmetric group of permutations of { 1,..., n }. In a recent paper [Random Structures Algorithms 29 (2006) 277-295] we showed that the weak law of large numbers holds for Z(n,kn,) if k(n) = o(n(2/5)); that is, lim(n ->infinity) Z (n,kn)/EZ(n,kn) = 1 in probability. The method of proof employed there used the second moment method and demonstrated that this method cannot ...
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作者：Hult, Henrik; Lindskog, Filip
作者单位：Brown University; Royal Institute of Technology
摘要：We study the extremal behavior of a stochastic integral driven by a multivariate Levy process that is regularly varying with index alpha > 0. For predictable integrands with a finite (alpha + delta)-moment, for some delta > 0, we show that the extremal behavior of the stochastic integral is due to one big jump of the driving Levy process and we determine its limit measure associated with regular variation on the space of cadlag functions.
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作者：Dembo, Amir; Peres, Yuval; Rosen, Jay
作者单位：Stanford University; Stanford University; City University of New York (CUNY) System; College of Staten Island (CUNY); University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：We show that the largest disccovered by a simple random walk (SRW) on Z(2) after n steps has radius n(1/4+o(1)), thus resolving an open problem of Revesz [Random Walk in Random and Non-Random Environments (1990) World Scientific, Teaneck, NJ]. For any fixed , the largest disc completely covered at least times by the SRW also has radius n(1/4+o(l)). However, the largest disc completely covered by each of E independent simple random walks on Z(2) after n steps is only of radius n (1/(2+2 root)+o...
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作者：Russo, Francesco; Trutnau, Gerald
作者单位：Universite Paris 13; University of Bielefeld
摘要：A new class of random partial differential equations of parabolic type is considered, where the stochastic term consists of an irregular noisy drift, not necessarily Gaussian, for which a suitable interpretation is provided. After freezing a realization of the drift (stochastic process), we study existence and uniqueness (in some appropriate sense) of the associated parabolic equation and a probabilistic interpretation is investigated.
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作者：Brossard, Jean; Leuridan, Christophe
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
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作者：Fang, Shizan; Imkeller, Peter; Zhang, Tusheng
作者单位：Universite Bourgogne Europe; Humboldt University of Berlin; University of Manchester
摘要：We consider stochastic differential equations driven by Wiener processes. The vector fields are supposed to satisfy only local Lipschitz conditions. The Lipschitz constants of the drift vector field, valid on balls of radius R, are supposed to grow not faster than log R, while those of the diffusion vector fields are supposed to grow not faster than root log R. We regularize the stochastic differential equations by associating with them approximating ordinary differential equations obtained by...
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作者：Limic, Vlada; Tarres, Pierre
作者单位：Aix-Marseille Universite; University of Oxford
摘要：The goal is to show that an edge-reinforced random walk on a graph of bounded degree, with reinforcement weight function W taken from a general class of reciprocally summable reinforcement weight functions, traverses a random attracting edge at all large times. The statement of the main theorem is very close to settling a conjecture of Sellke [Technical Report 94-26 (1994) Purdue Univ.]. An important corollary of this main result says that if W is reciprocally summable and nondecreasing, the a...
