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作者：Hoffmann, Marc; Ray, Kolyan
作者单位：Universite PSL; Universite Paris-Dauphine; Institut Universitaire de France; Imperial College London
摘要：We consider nonparametric Bayesian inference in a multidimensional diffusion model with reflecting boundary conditions based on discrete high-frequency observations. We prove a general posterior contraction rate theorem in L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>2$$\end{document}-loss, which is applie...
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作者：Debussche, Arnaud; Liu, Ruoyuan; Tzvetkov, Nikolay; Visciglia, Nicola
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes; University of Edinburgh; University of Edinburgh; Heriot Watt University; Ecole Normale Superieure de Lyon (ENS de LYON); University of Pisa
摘要：We consider the nonlinear Schr & ouml;dinger equation with multiplicative spatial white noise and an arbitrary polynomial nonlinearity on the two-dimensional full space domain. We prove global well-posedness by using a gauge-transform introduced by Hairer and Labb & eacute; (Electron Commun Probab 20(43):11, 2015) and constructing the solution as a limit of solutions to a family of approximating equations. This paper extends a previous result by Debussche and Martin (Nonlinearity 32(4):1147-11...
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作者：Bou-Rabee, Ahmed; Morfe, Peter S.
作者单位：University of Chicago
摘要：Pareto hull peeling is a discrete algorithm, generalizing convex hull peeling, for sorting points in Euclidean space. We prove that Pareto peeling of a random point set in two dimensions has a scaling limit described by a first-order Hamilton-Jacobi equation and give an explicit formula for the limiting Hamiltonian, which is both non-coercive and non-convex. This contrasts with convex peeling, which converges to curvature flow. The proof involves direct geometric manipulations in the same spir...
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作者：Rey, Lucas
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS)
摘要：The Doob transform technique enables the study of a killed random walk via a random walk with transition probabilities tilted by a discrete massive harmonic function. The main contribution of this paper is to transfer this powerful technique to statistical mechanics by relating two models, namely random rooted spanning forests (RSF) and random spanning trees (RST), and provide applications. More precisely, our first main theorem explicitly relates models on the level of partition functions, an...
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作者：Boedihardjo, March; Strohmer, Thomas; Vershynin, Roman
作者单位：Michigan State University; University of California System; University of California Davis; University of California System; University of California Irvine
摘要：Differential privacy is a mathematical concept that provides an information-theoretic security guarantee. While differential privacy has emerged as a de facto standard for guaranteeing privacy in data sharing, the known mechanisms to achieve it come with some serious limitations. Utility guarantees are usually provided only for a fixed, a priori specified set of queries. Moreover, there are no utility guarantees for more complex-but very common-machine learning tasks such as clustering or clas...
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作者：Olesker-Taylor, Sam; Zanetti, Luca
作者单位：University of Warwick; University of Bath
摘要：In the Fastest Mixing Markov Chain problem, we are given a graph G = (V, E) and desire the discrete-time Markov chain with smallest mixing time tau subject to having equilibrium distribution uniform on V and non-zero transition probabilities only across edges of the graph. It is well-known that the mixing time tau(RW) of the lazy random walk on G is characterised by the edge conductance Phi of G via Cheeger's inequality: Phi(-1) less than or similar to tau(RW) less than or similar to Phi(-2) l...
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作者：Cass, Thomas; Ferrucci, Emilio
作者单位：Imperial College London; University of Oxford
摘要：We compute the Wiener chaos decomposition of the signature for a class of Gaussian processes, which contains fractional Brownian motion (fBm) with Hurst parameter H is an element of (1/4,1). At level 0, our result yields an expression for the expected signature of such processes, which determines their law (Chevyrev and Lyons in Ann Probab 44(6):4049-4082, 2016). In particular, this formula simultaneously extends both the one for 1/2 < H-fBm (Baudoin and Coutin in Stochast Process Appl 117(5):...
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作者：Vidmar, Matija; Warren, Jon
作者单位：University of Ljubljana; University of Warwick
摘要：The times of Brownian local minima, maxima and their union are three distinct examples of local, stationary, dense, random countable sets associated with classical Wiener noise. Being local means, roughly, determined by the local behavior of the sample paths of the Brownian motion, and stationary means invariant relative to the Levy shifts of the sample paths. We answer to the affirmative Tsirelson's question, whether or not there are any others, and develop some general theory for such sets. ...
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作者：Goncalves, P.; Jara, M.; Marinho, R.; Menezes, O.
作者单位：Universidade de Lisboa; Universidade Federal de Santa Maria (UFSM); Universidade Federal da Bahia
摘要：We study the scaling properties of the non-equilibrium stationary states (NESS) of a reaction-diffusion model. Under a suitable smallness condition, we show that the density of particles satisfies a law of large numbers with respect to the NESS, with an explicit rate of convergence, and we also show that at mesoscopic scales the NESS is well approximated by a local equilibrium (product) measure, in the total variation distance. In addition, in dimensions d <= 3\documentclass[12pt]{minimal} \us...
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作者：Riera, Armand; Rosales-Ortiz, Alejandro
作者单位：Universite Paris Cite; Sorbonne Universite; University of Zurich
摘要：We construct an additive functional playing the role of the local time-at a fixed point x-for Markov processes indexed by Levy trees. We start by proving that Markov processes indexed by Levy trees satisfy a special Markov property which can be thought as a spatial version of the classical Markov property. Then, we construct our additive functional by an approximation procedure and we characterize the support of its Lebesgue-Stieltjes measure. We also give an equivalent construction in terms o...
