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作者：Harris, Simon C.; Johnston, Samuel G. G.; Roberts, Matthew I.
作者单位：University of Auckland; University College Dublin; University of Bath
摘要：Take a continuous-time Galton-Watson tree. If the system survives until a large time T, then choose k particles uniformly from those alive. What does the ancestral tree drawn out by these k particles look like? Some special cases are known but we give a more complete answer. We concentrate on near-critical cases where the mean number of offspring is 1 + mu/T for some mu is an element of R, and show that a scaling limit exists as T -> infinity. Viewed backwards in time, the resulting coalescent...
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作者：Caye, Thomas; Herdegen, Martin; Muhle-Karbe, Johannes
作者单位：Dublin City University; University of Warwick; Imperial College London
摘要：We study portfolio choice with small nonlinear price impact on general market dynamics. Using probabilistic techniques and convex duality, we show that the asymptotic optimum can be described explicitly up to the solution of a nonlinear ODE, which identifies the optimal trading speed and the performance loss due to the trading friction. Previous asymptotic results for proportional and quadratic trading costs are obtained as limiting cases. As an illustration, we discuss how nonlinear trading c...
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作者：Baik, Jinho; Bothner, Thomas
作者单位：University of Michigan System; University of Michigan; University of London; King's College London
摘要：The real Ginibre ensemble consists of n x n real matrices X whose entries are i.i.d. standard normal random variables. In sharp contrast to the complex and quaternion Ginibre ensemble, real eigenvalues in the real Ginibre ensemble attain positive likelihood. In turn, the spectral radius R-n = max(1 <= j <= n) vertical bar z(j)(X)vertical bar of the eigenvalues z(j)(X) is an element of C of a real Ginibre matrix X follows a different limiting law (as n -> infinity) for z(j) (X) is an element of...
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作者：Fang, Wei; Giles, Michael B.
作者单位：University of Oxford
摘要：This paper proposes an adaptive timestep construction for an Euler-Maruyama approximation of SDEs with nonglobally Lipschitz drift. It is proved that if the timestep is bounded appropriately, then over a finite time interval the numerical approximation is stable, and the expected number of timesteps is finite. Furthermore, the order of strong convergence is the same as usual, that is, order 1/2 for SDEs with a nonuniform globally Lipschitz volatility, and order 1 for Langevin SDEs with unit vo...
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作者：Hermon, Jonathan; Ben Morris; Qin, Chuan; Sly, Allan
作者单位：University of Cambridge; University of California System; University of California Davis; Princeton University
摘要：Given an infinite connected regular graph G = (V, E), place at each vertex Poisson(lambda) walkers performing independent lazy simple random walks on G simultaneously. When two walkers visit the same vertex at the same time they are declared to be acquainted. We show that when G is vertex-transitive and amenable, for all lambda > 0 a.s. any pair of walkers will eventually have a path of acquaintances between them. In contrast, we show that when G is nonamenable (not necessarily transitive) the...
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作者：Bardenet, Remi; Hardy, Adrien
作者单位：Universite de Lille; Centrale Lille; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Information Sciences & Technologies (INS2I); Universite de Lille; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Inria
摘要：We show that repulsive random variables can yield Monte Carlo methods with faster convergence rates than the typical N-1/2, where N is the number of integrand evaluations. More precisely, we propose stochastic numerical quadratures involving determinantal point processes associated with multivariate orthogonal polynomials, and we obtain root mean square errors that decrease as N-(1+1/ d)/2, where d is the dimension of the ambient space. First, we prove a central limit theorem (CLT) for the lin...
