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作者：Rider, Brian; Sinclair, Christopher D.
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University; University of Oregon
摘要：The real Ginibre ensemble refers to the family of n x n matrices in which each entry is an independent Gaussian random variable of mean zero and variance one. Our main result is that the appropriately scaled spectral radius converges in law to a Gumbel distribution as n -> infinity. This fact has been known to hold in the complex and quaternion analogues of the ensemble for some time, with simpler proofs. Along the way we establish a new form for the limit law of the largest real eigenvalue.
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作者：Faure, Mathieu; Schreiber, Sebastian J.
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Aix-Marseille Universite; University of California System; University of California Davis
摘要：We analyze quasi-stationary distributions {mu(epsilon)}(epsilon>0) of a family of Markov chains {X-epsilon}(epsilon>0) that are random perturbations of a bounded, continuous map F : M -> M, where M is a closed subset of R-k. Consistent with many models in biology, these Markov chains have a closed absorbing set M-0 subset of M such that F(M-0) = M-0 and F (M \ M-0) = M \ M-0. Under some large deviations assumptions on the random perturbations, we show that, if there exists a positive attractor...
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作者：Jahnel, Benedikt; Kuelske, Christof
作者单位：Ruhr University Bochum
摘要：We consider a class of discrete q-state spin models defined in terms of a translation-invariant quasilocal specification with discrete clock-rotation invariance which have extremal Gibbs measures mu(1)(phi) labeled by the uncountably many values of phi in the one-dimensional sphere (introduced by van Enter, Opoku, Kulske [J. Phys. A 44 (2011) 475002, 11]). In the present paper we construct an associated Markov jump process with quasilocal rates whose semigroup (S-t)(t >= 0) acts by a continuou...
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作者：Bayer, Christian; Schoenmakers, John
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：In this paper we derive stochastic representations for the finite dimensional distributions of a multidimensional diffusion on a fixed time interval, conditioned on the terminal state. The conditioning can be with respect to a fixed point or more generally with respect to some subset. The representations rely on a reverse process connected with the given (forward) diffusion as introduced in Milstein, Schoenmakers and Spokoiny [Bernoulli 10 (2004) 281-312] in the context of a forward-reverse tr...
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作者：Lucon, Eric; Stannat, Wilhelm
作者单位：Technical University of Berlin
摘要：Motivated by considerations from neuroscience (macroscopic behavior of large ensembles of interacting neurons), we consider a population of mean field interacting diffusions in R-m in the presence of a random environment and with spatial extension: each diffusion is attached to one site of the lattice Z(d), and the interaction between two diffusions is attenuated by a spatial weight that depends on their positions. For a general class of singular weights (including the case already considered ...
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作者：Giles, Michael B.; Szpruch, Lukasz
作者单位：University of Oxford
摘要：In this paper we introduce a new multilevel Monte Carlo (MLMC) estimator for multi-dimensional SDEs driven by Brownian motions. Giles has previously shown that if we combine a numerical approximation with strong order of convergence O(Delta t) with MLMC we can reduce the computational complexity to estimate expected values of functionals of SDE solutions with a root-mean-square error of epsilon from O(epsilon(-3)) to O(epsilon(-2)). However, in general, to obtain a rate of strong convergence h...
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作者：Berestycki, Julien; Berestycki, Nathanael; Limic, Vlada
作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Cambridge; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：We describe a new general connection between Lambda-coalescents and genealogies of continuous-state branching processes. This connection is based on the construction of an explicit coupling using a particle representation inspired by the lookdown process of Donnelly and Kurtz. This coupling has the property that the coalescent comes down from infinity if and only if the branching process becomes extinct, thereby answering a question of Bertoin and Le Gall. The coupling also offers new perspect...
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作者：Todorov, Viktor; Tauchen, George
作者单位：Northwestern University; Duke University
摘要：We derive limit theorems for. the empirical distribution function of de-volatilized increments of an Ito semimartingale observed at high frequencies. These devolatilized increments are formed by suitably rescaling and truncating the raw increments to remove the effects of stochastic volatility and large jumps. We derive the limit of the empirical c.d.f. of the adjusted increments for any Ito semimartingale whose dominant component at high frequencies has activity index of 1 < beta <= 2, where ...
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作者：Beskos, Alexandros; Crisan, Dan; Jasra, Ajay
作者单位：National University of Singapore; University of London; University College London; Imperial College London
摘要：We investigate the stability of a Sequential Monte Carlo (SMC) method applied to the problem of sampling from a target distribution on R-d for large d. It is well known [Bengtsson, Bickel and Li, In Probability and Statistics: Essays in Honor of David A. Freedman, D. Nolan and T. Speed, eds. (2008) 316-334 IMS; see also Pushing the Limits of Contemporary Statistics (2008) 318-329 IMS, Mon. Weather Rev. (2009) 136 (2009) 4629-4640] that using a single importance sampling step, one produces an a...
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作者：Foss, Sergey; Martin, James B.; Schmidt, Philipp
作者单位：Heriot Watt University; Russian Academy of Sciences; University of Oxford
摘要：We consider directed last-passage percolation on the random graph G = (V, E) where V = Z and each edge (i, j), for i < j is an element of Z, is present in E independently with some probability p is an element of (0, 1]. To every (i, j) is an element of E we attach i.i.d. random weights v(i, j) > 0. We are interested in the behaviour of w(0,n), which is the maximum weight of all directed paths from 0 to n, as n -> infinity. We see two very different types of behaviour, depending on whether E[v(...
