2期

最新文章

• LIMIT DISTRIBUTION THEORY FOR SMOOTH p-WASSERSTEIN DISTANCES AI翻译
  作者：Goldfeld, Ziv; Kato, Kengo; Nietert, Sloan; Rioux, Gabriel
  作者单位：Cornell University; Cornell University; Cornell University; Cornell University
  摘要：The Wasserstein distance is a metric on a space of probability measures that has seen a surge of applications in statistics, machine learning, and applied mathematics. However, statistical aspects of Wasserstein distances are bottlenecked by the curse of dimensionality, whereby the number of data points needed to accurately estimate them grows exponentially with dimension. Gaussian smoothing was recently introduced as a means to alleviate the curse of dimensionality, giving rise to a parametri...
• ON A RANDOM MODEL OF FORGETTING AI翻译
  作者：Alon, Noga; Elboim, Dor; Sly, Allan
  作者单位：Princeton University
  摘要：Georgiou, Katkov and Tsodyks considered the following random process. Let x(1), x(2), . . . be an infinite sequence of independent, identically distributed, uniform random points in [0, 1]. Starting with S = {0}, the elements x(k) join S one by one, in order. When an entering element is larger than the current minimum element of S, this minimum leaves S. Let S(1, n) denote the content of S after the first n elements x(k) join. Simulations suggest that the size |S(1, n)| of S at time n is typic...
• FIRST PASSAGE PERCOLATION WITH LONG-RANGE CORRELATIONS AND APPLICATIONS TO RANDOM SCHRÖDINGER OPERATORS AI翻译
  作者：Andres, Sebastian; Prevost, Alexis
  作者单位：Braunschweig University of Technology; University of Geneva
  摘要：We consider first passage percolation (FPP) with passage times generated by a general class of models with long-range correlations on Zd, d >= 2, including discrete Gaussian free fields, Ginzburg-Landau backward difference phi interface models or random interlacements as prominent examples. We show that the associated time constant is positive, the FPP distance is comparable to the Euclidean distance, and we obtain a shape theorem. We also present two applications for random conductance models...
• An entropic approach for Hamiltonian Monte Carlo: The idealized case AI翻译
  作者：Monmarche, Pierre
  作者单位：Sorbonne Universite; Sorbonne Universite; Universite Paris Cite
  摘要：Quantitative long-time entropic convergence and short-time regularization are established for an idealized Hamiltonian Monte Carlo chain which alternatively follows an Hamiltonian dynamics for a fixed time and then partially or totally refreshes its velocity with an auto-regressive Gaussian step. These results, in discrete time, are the analogues of similar results for the continuous-time kinetic Langevin diffusion, and the latter can be obtained from our bounds in a suitable limit regime. The...
• THE NEUMANN PROBLEM FOR FULLY NONLINEAR SPDE AI翻译
  作者：Gassiat, Paul; Seeger, Benjamin
  作者单位：Universite PSL; Universite Paris-Dauphine; University of Texas System; University of Texas Austin
  摘要：We generalize the notion of pathwise viscosity solutions, put forward by Lions and Souganidis to study fully nonlinear stochastic partial differential equations, to equations set on a sub-domain with Neumann boundary conditions. Under a convexity assumption on the domain, we obtain a comparison theorem which yields existence and uniqueness of solutions as well as continuity with respect to the driving noise. As an application, we study the long time behaviour of a stochastically perturbed mean...
• MCKEAN-VLASOV SDE AND SPDE WITH LOCALLY MONOTONE COEFFICIENTS AI翻译
  作者：Hong, Wei; Hu, Shanshan; Liu, Wei
  作者单位：Jiangsu Normal University; University of Bielefeld
  摘要：In this paper we mainly investigate the strong and weak well-posedness of a class of McKean-Vlasov stochastic (partial) differential equations. The main existence and uniqueness results state that we only need to impose some local assumptions on the coefficients, that is, locally monotone condition both in state variable and distribution variable, which cause some essential difficulty since the coefficients of McKean-Vlasov stochastic equations typically are nonlocal. Furthermore, the large de...
• THE STEFAN PROBLEM AND FREE TARGETS OF OPTIMAL BROWNIANMARTINGALE TRANSPORT AI翻译
  作者：Kim, Inwon C.; Kim, Young-Heon
  作者单位：University of California System; University of California Los Angeles; University of British Columbia
  摘要：e formulate and solve a free target optimal Brownian stopping prob-lem from a given distribution while the target distribution is free and is con-ditioned to satisfy a given density height constraint. The free target optimiza-tion problem exhibits monotonicity, from which a remarkable universalityfollows, in the sense that the optimal target is independent of its Lagrangiancost type. In particular, the solutions to this optimization problem generatesolutions to both unstable and stable type of...
• LINEAR-TIME UNIFORM GENERATION OF RANDOM SPARSE CONTINGENCY TABLES WITH SPECIFIED MARGINALS AI翻译
  作者：Arman, Andrii; Gao, Pu; Wormald, Nicholas
  作者单位：University of Manitoba; University of Waterloo; Monash University
  摘要：We give an algorithm which generates a uniformly random contingency table with specified marginals, that is, a matrix with nonnegative integer values and specified row and column sums. Such algorithms are useful in statistics and combinatorics. When Delta(4) < M/5, where Delta is the maximum of the row and column sums and M is the sum of all entries of the matrix, our algorithm runs in time linear in M in expectation. Most previously published algorithms for this problem are approximate sample...
• AN EXPLICIT MILSTEIN-TYPE SCHEME FOR INTERACTING PARTICLESYSTEMS AND MCKEAN-VLASOV SDES WITH COMMON NOISE ANDNON-DIFFERENTIABLE DRIFT COEFFICIENTS AI翻译
  作者：Biswas, Sani; Kumar, Chaman; Neelima; Dos Reis, Goncalo; Reisinger, Christoph
  作者单位：Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Roorkee; University of Delhi; University of Edinburgh; University of Oxford
  摘要：We propose an explicit drift-randomised Milstein scheme for bothMcKean-Vlasov stochastic differential equations and associated high-dimen-sional interacting particle systems with common noise. By using a driftrandomisation step in space and measure, we establish the scheme's strongconvergence rate of 1 under reduced regularity assumptions on the drift co-efficient: no classical (Euclidean) derivatives in space or measure derivatives(e.g., Lions/Frechet) are required. The main result is establi...
• A FEASIBLE CENTRAL LIMIT THEOREM FOR REALISED COVARIATION OF SPDES IN THE CONTEXT OF FUNCTIONAL DATA AI翻译
  作者：Benth, Fred espen; Schroers, Dennis; Veraart, Almut e. d.
  作者单位：University of Oslo; Imperial College London
  摘要：This article establishes an asymptotic theory for volatility estimation in an infinite -dimensional setting. We consider mild solutions of semilinear stochastic partial differential equations and derive a stable central limit theorem for the semigroup-adjusted realised covariation (SARCV), which is a consistent estimator of the integrated volatility and a generalisation of the realised quadratic covariation to Hilbert spaces. Moreover, we introduce semigroup-adjusted multipower variations (SAM...