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作者：Szpruch, Lukasz; Tse, Alvin
作者单位：University of Edinburgh
摘要：Let mu is an element of P-2(R-d), where P-2(R-d) denotes the space of square integrable probability measures, and consider a Borel-measurable function Phi : P-2(R-d) -> R. In this paper we develop an antithetic Monte Carlo estimator (A-MLMC) for Phi(mu), which achieves sharp error bound under mild regularity assumptions. The estimator takes as input the empirical laws mu(N) = 1/N Sigma(N)(i =1) delta X-i, where (a) (X-i)(i =1)(N) is a sequence of i.i.d. samples from mu or (b) (X-i)(i =1)(N) is...
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作者：Altmeyer, Randolf; Reiss, Markus
作者单位：Humboldt University of Berlin
摘要：The coefficient function of the leading differential operator is estimated from observations of a linear stochastic partial differential equation (SPDE). The estimation is based on continuous time observations which are localised in space. For the asymptotic regime with fixed time horizon and with the spatial resolution of the observations tending to zero, we provide rate-optimal estimators and establish scaling limits of the deterministic PDE and of the SPDE on growing domains. The estimators...
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作者：Dembo, Amir; Lubetzky, Eyal; Zeitouni, Ofer
作者单位：Stanford University; Stanford University; New York University; Weizmann Institute of Science
摘要：We study dynamics for asymmetric spin glass models, proposed by Hertz et al. and Sompolinsky et al. in the 1980's in the context of neural networks: particles evolve via a modified Langevin dynamics for the Sherrington-Kirkpatrick model with soft spins, whereby the disorder is i.i.d. standard Gaussian rather than symmetric. Ben Arous and Guionnet (Probab. Theory Related Fields 102 (1995) 455-509), followed by Guionnet (Probab. Theory Related Fields 109 (1997) 183-215), proved for Gaussian inte...
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作者：Broman, Erik, I; Elias, Olof; Mussini, Filipe; Tykesson, Johan
作者单位：Chalmers University of Technology; University of Gothenburg; Uppsala University
摘要：We consider a semi-scale invariant version of the Poisson cylinder model which in a natural way induces a random fractal set. We show that this random fractal exhibits an existence phase transition for any dimension d >= 2, and a connectivity phase transition whenever d >= 4. We determine the exact value of the critical point of the existence phase transition, and we show that the fractal set is almost surely empty at this critical point. A key ingredient when analysing the connectivity phase ...
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作者：Bate, Michael E.; Connor, Stephen B.; Matheau-Raven, Oliver
作者单位：University of York - UK
摘要：We introduce a new type of card shuffle called one-sided transpositions. At each step a card is chosen uniformly from the pack and then transposed with another card chosen uniformly from below it. This defines a random walk on the symmetric group generated by a distribution which is nonconstant on the conjugacy class of transpositions. Nevertheless, we provide an explicit formula for all eigenvalues of the shuffle by demonstrating a useful correspondence between eigenvalues and standard Young ...
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作者：Kroshnin, Alexey; Spokoiny, Vladimir; Suvorikova, Alexandra
作者单位：Russian Academy of Sciences; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：In this work we introduce the concept of Bures-Wasserstein barycenter Q(*), that is essentially a Frechet mean of some distribution P supported on a subspace of positive semi-definite d-dimensional Hermitian operators H+(d). We allow a barycenter to be constrained to some affine subspace of H+(d), and we provide conditions ensuring its existence and uniqueness. We also investigate convergence and concentration properties of an empirical counterpart of Q(*) in both Frobenius norm and Bures-Wass...
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作者：Rockner, Michael; Yang, Huanyu; Zhu, Rongchan
作者单位：University of Bielefeld; Free University of Berlin; Beijing Institute of Technology
摘要：We consider the stochastic two-dimensional Cahn-Hilliard equation which is driven by the derivative in space of a space-time white noise. We use two different approaches to study this equation. First we prove that there exists a unique solution Y to the shifted equation (1.4). Then X := Y + Z is the unique solution to the stochastic Cahn-Hilliard equation, where Z is the corresponding O-U process. Moreover, we use the Dirichlet form approach in (Probab. Theory Related Fields 89 (1991) 347-386)...
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作者：Lagarias, Jeffrey C.; Rodgers, Brad
作者单位：University of Michigan System; University of Michigan; Queens University - Canada
摘要：We say that one point process on the line R mimics another at a band-width B if for each n >= 1 the two point processes have n-level correlation functions that agree when integrated against all band-limited test functions on bandwidth [-B, B]. This paper asks the question of for what values a and B can a given point process on the real line be mimicked at bandwidth B by a point process supported on the lattice aZ. For Poisson point processes we give a complete answer for allowed parameter rang...
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作者：de Menibus, Benjamin Hellouin; Le Borgne, Yvan
作者单位：Universite Paris Saclay; Universite de Bordeaux
摘要：The one-dimensional three-state cyclic cellular automaton is a simple spatial model with three states in a cyclic rock-paper-scissors preypredator relationship. Starting from a random configuration, similar states gather in increasingly large clusters; asymptotically, any finite region is filled with a uniform state that is, after some time, driven out by its predator, each state taking its turn in dominating the region (heteroclinic cycles). We consider the situation where each site in the in...
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作者：Kardaras, Constantinos; Robertson, Scott
作者单位：University of London; London School Economics & Political Science; Boston University
摘要：We consider the problem of robustly maximizing the growth rate of investor wealth in the presence of model uncertainty. Possible models are all those under which the assets' region E and instantaneous covariation c are known, and where the assets are stable with an exogenously given limiting density p, in that their occupancy time measures converge to a law governed by p. This latter assumption is motivated by the observed stability of ranked relative market capitalizations for equity markets....
