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作者：Chen, Zhen-Qing; Zhang, Xicheng
作者单位：University of Washington; University of Washington Seattle; Wuhan University
摘要：Let d >= 1 and alpha epsilon (0, 2). Consider the following non-local and nonsymmetric Levy-type operator on R-d : L-alpha(kappa) f(x) := p.v. integral(Rd) (f (x + z) - f (x))kappa(x, z)/vertical bar z vertical bar(d+alpha) dz, where 0 < kappa(0) <= kappa(x, z) <= kappa(1), kappa(x, z) = kappa(x,-z), and vertical bar kappa(x, z) - kappa(y, z) <= kappa(2)vertical bar x -y vertical bar(beta) for some beta is an element of(0, 1). Using Levi's method, we construct the fundamental solution (also ca...
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作者：Gueneysu, Batu; Keller, Matthias; Schmidt, Marcel
作者单位：Humboldt University of Berlin; Hebrew University of Jerusalem; Friedrich Schiller University of Jena
摘要：In this paper we prove a Feynman-Kac-It formula for magnetic Schrodinger operators on arbitrary weighted graphs. To do so, we have to provide a natural and general framework both on the operator theoretic and the probabilistic side of the equation. On the operator side we identify a very general class of potentials that allows the definition of magnetic Schrodinger operators. On the probabilistic side, we introduce an appropriate notion of stochastic line integrals with respect to magnetic pot...
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作者：Talagrand, Michel
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：The author has recently introduced a mean-field spin glass model with infinite connectivity Talagrand (Mean Field Models for Spin Glasses. Springer, Berlin, 2011) that has the striking property that one of the parameters naturally occurring in the replica-symmetric equations is a function. We introduce a version of this model where the interaction is diluted, and where at high temperature the computation of the typical value of the overlaps requires the use of a random measure as an auxiliary ...
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作者：Donoho, David; Montanari, Andrea
作者单位：Stanford University; Stanford University
摘要：In a recent article, El Karoui et al. (Proc Natl Acad Sci 110(36):14557-14562, 2013) study the distribution of robust regression estimators in the regime in which the number of parameters p is of the same order as the number of samples n. Using numerical simulations and 'highly plausible' heuristic arguments, they unveil a striking new phenomenon. Namely, the regression coefficients contain an extra Gaussian noise component that is not explained by classical concepts such as the Fisher informa...
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作者：Deya, Aurelien
作者单位：Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS)
摘要：We use the formalism of Hairer's regularity structures theory to study a heat equation model with non-linear perturbation driven by a space-time fractional noise. Different regimes are observed, depending on the global pathwise roughness of the noise. To this end, and following the procedure exhibited in Hairer [Invent Math 198(2):269-504, (2014)], the equation is first lifted into some abstract regularity structure and therein solved through a fixed-point argument. Then we construct a consist...
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作者：Karatzas, Ioannis; Ruf, Johannes
作者单位：Columbia University; University of London; University College London
摘要：We study the distribution of the time to explosion for one-dimensional diffusions. We relate this question to the computation of expectations of suitable nonnegative local martingales. Moreover, we characterize the distribution function of the time to explosion as the minimal solution to a certain Cauchy problem for an appropriate parabolic differential equation; this leads to alternative characterizations of Feller's criterion for explosions. We discuss in detail several examples for which it...
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作者：Champagnat, Nicolas; Villemonais, Denis
作者单位：Universite de Lorraine; Inria
摘要：For general, almost surely absorbed Markov processes, we obtain necessary and sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process (the process conditioned to never be absorbed). We apply these results to one-dimensional birth and death processeswith catastrophes, multi-dimensional birth and death processes, infinite-dimensional population m...
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作者：Strauch, Claudia
作者单位：University of Hamburg
摘要：The problem of pointwise adaptive estimation of the drift coefficient of a multivariate diffusion process is investigated. We propose an estimator which is sharp adaptive on scales of Sobolev smoothness classes. The analysis of the exact risk asymptotics allows to identify the impact of the dimension and other influencing values-such as the geometry of the diffusion coefficient-of the prototypical drift estimation problem for a large class of multidimensional diffusion processes. We further sk...
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作者：Morters, Peter; Redl, Istvan
作者单位：University of Bath
摘要：Let (X-n : n is an element of Z) be a two-sided recurrent Markov chain with fixed initial state and let be a probability measure on its state space. We give a necessary and sufficient criterion for the existence of a non-randomized time T such that has the law of the same Markov chain with initial distribution . In the case when our criterion is satisfied we give an explicit solution, which is also a stopping time, and study its moment properties. We show that this solution minimizes the expec...
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作者：Miller, Jason; Sheffield, Scott
作者单位：Microsoft; Massachusetts Institute of Technology (MIT); University of Cambridge
摘要：Fix constants and , and let h be an instance of the Gaussian free field on a planar domain. We study flow lines of the vector field starting at a fixed boundary point of the domain. Letting vary, one obtains a family of curves that look locally like processes with (where ), which we interpret as the rays of a random geometry with purely imaginary curvature. We extend the fundamental existence and uniqueness results about these paths to the case that the paths intersect the boundary. We also sh...
