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作者：Chatterjee, Shirshendu; Durrett, Rick
作者单位：Cornell University; Duke University
摘要：Aldous [(2007) Preprint] defined a gossip process in which space is a discrete N x N torus, and the state of the process at time t is the set of individuals who know the information. Information spreads from a site to its nearest neighbors at rate 1/4 each and at rate N(-alpha) to a site chosen at random from the torus. We will be interested in the case in which alpha < 3, where the long range transmission significantly accelerates the time at which everyone knows the information. We prove thr...
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作者：Chen, Xinfu; Cheng, Lan; Chadam, John; Saunders, David
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh; State University of New York (SUNY) System; SUNY Fredonia; University of Waterloo
摘要：We study the inverse boundary crossing problem for diffusions. Given a diffusion process X-t, and a survival distribution p on [0,8), we demonstrate that there exists a boundary b(t) such that p(t) = P [tau > t], where t is the first hitting time of X-t to the boundary b(t). The approach taken is analytic, based on solving a parabolic variational inequality to find b. Existence and uniqueness of the solution to this variational inequality were proven in earlier work. In this paper, we demonstr...
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作者：Shkolnikov, Mykhaylo
作者单位：Stanford University
摘要：We consider finite and infinite systems of particles on the real line and half-line evolving in continuous time. Hereby, the particles are driven by i.i.d. Levy processes endowed with rank-dependent drift and diffusion coefficients. In the finite systems we show that the processes of gaps in the respective particle configurations possess unique invariant distributions and prove the convergence of the gap processes to the latter in the total variation distance, assuming a bound on the jumps of ...
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作者：Cuchiero, Christa; Filipovic, Damir; Mayerhofer, Eberhard; Teichmann, Josef
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Swiss Finance Institute (SFI)
摘要：This article provides the mathematical foundation for stochastically continuous affine processes on the cone of positive semidefinite symmetric matrices. This analysis has been motivated by a large and growing use of matrix-valued affine processes in finance, including multi-asset option pricing with stochastic volatility and correlation structures, and fixed-income models with stochastically correlated risk factors and default intensities.
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作者：Taflin, Erik
作者单位：CY Cergy Paris Universite; Ecole Internationale des Sciences du Traitement de linformation; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We construct Zero-Coupon Bond markets driven by a cylindrical Brownian motion in which the notion of generalized portfolio has important flaws: There exist bounded smooth random variables with generalized hedging portfolios for which the price of their risky part is +infinity at each time. For these generalized portfolios, sequences of the prices of the risky part of approximating portfolios can be made to converges to any given extended real number in [-infinity, infinity].
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作者：Como, Giacomo; Fagnani, Fabio
作者单位：Massachusetts Institute of Technology (MIT); Polytechnic University of Turin
摘要：Scaling limits are analyzed for stochastic continuous opinion dynamics systems, also known as gossip models. In such models, agents update their vector-valued opinion to a convex combination (possibly agent- and opinion-dependent) of their current value and that of another observed agent. It is shown that, in the limit of large agent population size, the empirical opinion density concentrates, at an exponential probability rate, around the solution of a probability-measure-valued ordinary diff...
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作者：Hairer, Martin; Stuart, Andrew M.; Voss, Jochen
作者单位：University of Warwick; University of Leeds
摘要：A series of recent articles introduced a method to construct stochastic partial differential equations (SPDEs) which are invariant with respect to the distribution of a given conditioned diffusion. These works are restricted to the case of elliptic diffusions where the drift has a gradient structure and the resulting SPDE is of second-order parabolic type. The present article extends this methodology to allow the construction of SPDEs which are invariant with respect to the distribution of a c...
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作者：Balogh, Jozsef; Bollobas, Bela; Krivelevich, Michael; Muller, Tobias; Walters, Mark
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; Tel Aviv University; University of Cambridge; University of London
摘要：We prove that, in the Gilbert model for a random geometric graph, almost every graph becomes Hamiltonian exactly when it first becomes 2-connected. This answers a question of Penrose. We also show that in the k-nearest neighbor model, there is a constant. such that almost every kappa-connected graph has a Hamilton cycle.
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作者：Collevecchio, Andrea; Schmitz, Tom
作者单位：Universita Ca Foscari Venezia; Max Planck Society
摘要：We develop a technique that provides a lower bound on the speed of transient random walk in a random environment on regular trees. A refinement of this technique yields upper bounds on the first regeneration level and regeneration time. In particular, a lower and upper bound on the covariance in the annealed invariance principle follows. We emphasize the fact that our methods are general and also apply in the case of once-reinforced random walk. Durrett, Kesten and Limic [Probab. Theory Relate...
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作者：Kendall, Wilfrid S.
作者单位：University of Warwick
摘要：The stationary isotropic Poisson line process was used to derive upper bounds on mean excess network geodesic length in Aldous and Kendall [Adv. in Appl. Probab. 40 (2008) 1-21]. The current paper presents a study of the geometry and fluctuations of near-geodesics in the network generated by the line process. The notion of a Poissonian city is introduced, in which connections between pairs of nodes are made using simple no-overshoot paths based on the Poisson line process. Asymptotics for geom...
