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最新文章

• OPTIMAL STOPPING WITH SIGNATURES AI翻译
  作者：Bayer, Christian; Hager, Paul P.; Riedel, Sebastian; Schoenmakers, John
  作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Humboldt University of Berlin; Fern University Hagen
  摘要：We propose a new method for solving optimal stopping problems (such as American option pricing in finance) under minimal assumptions on the un-derlying stochastic process X. We consider classic and randomized stopping times represented by linear and nonlinear functionals of the rough path sig-nature X
• FUNCTIONAL CENTRAL LIMIT THEOREMS FOR WIGNER MATRICES AI翻译
  作者：Cipolloni, Giorgio; Erdos, Laszlo; Schroder, Dominik
  作者单位：Institute of Science & Technology - Austria; Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：We consider the fluctuations of regular functions f of a Wigner matrix W viewed as an entire matrix f (W). Going beyond the well-studied tra-cial mode, Tr f (W), which is equivalent to the customary linear statistics of eigenvalues, we show that Tr f (W)A is asymptotically normal for any nontrivial bounded deterministic matrix A. We identify three different and asymptotically independent modes of this fluctuation, corresponding to the tracial part, the traceless diagonal part and the off-diago...
• TRANSITIVE CLOSURE IN A POLLUTED ENVIRONMENT AI翻译
  作者：Gravner, Janko; Kolesnik, Brett
  作者单位：University of California System; University of California Davis; University of California System; University of California San Diego
  摘要：We introduce and study a new percolation model, inspired by recent works on jigsaw percolation, graph bootstrap percolation, and percolation in polluted environments. Start with an oriented graph G0 of initially occu-pied edges on n vertices, and iteratively occupy additional (oriented) edges by transitivity, with the constraint that only open edges in a certain random set can ever be occupied. All other edges are closed, creating a set of obsta-cles for the spread of occupied edges. When G0 i...
• ON A NONLINEAR SPDE DERIVED FROM A HYDRODYNAMIC LIMIT IN A SINAI-TYPE RANDOM ENVIRONMENT AI翻译
  作者：Landim, Claudio; Pacheco, Carlos G.; Sethuraman, Sunder; Xue, Jianfei
  作者单位：Instituto Politecnico Nacional - Mexico; CINVESTAV - Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional; University of Arizona; University of Missouri System; University of Missouri Columbia
  摘要：With the recent developments on nonlinear SPDEs, where smoothing of rough noises is needed, one is naturally led to study interacting particle systems whose macroscopic evolution is described by these equations and which possess an in-built smoothing. In this article, our main results are to derive regularized versions of the ill-posed one-dimensional SPDE partial derivative(t)rho = 1/2 Delta Phi(rho) - 2 del (W'Phi(rho)),where the spatial white noise W' is replaced by a regularization W'epsil...
• UNADJUSTED LANGEVIN ALGORITHM WITH MULTIPLICATIVE NOISE: TOTAL VARIATION AND WASSERSTEIN BOUNDS AI翻译
  作者：Pages, Gilles; Panloup, Fabien
  作者单位：Universite Paris Cite; Sorbonne Universite; Universite d'Angers; Centre National de la Recherche Scientifique (CNRS)
  摘要：In this paper, we focus on nonasymptotic bounds related to the Euler scheme of an ergodic diffusion with a possibly multiplicative diffusion term (nonconstant diffusion coefficient). More precisely, the objective of this paper is to control the distance of the standard Euler scheme with decreasing step (usually called unadjusted Langevin algorithm in the Monte Carlo literature) to the invariant distribution of such an ergodic diffusion. In an appropriate Lyapunov setting and under uniform elli...
• EXTENDED L-ENSEMBLES: A NEW REPRESENTATION FOR DETERMINANTAL POINT PROCESSES AI翻译
  作者：Tremblay, Nicolas; Barthelme, Simon; Usevich, Konstantin; Amblard, Pierre-Olivier
  作者单位：Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Universite de Lorraine; Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS)
  摘要：Determinantal point processes (DPPs) are a class of repulsive point pro-cesses, popular for their relative simplicity. They are traditionally defined via their marginal distributions, but a subset of DPPs called L-ensembles have tractable likelihoods and are thus particularly easy to work with. Indeed, in many applications, DPPs are more naturally defined based on the L-ensemble formulation rather than through the marginal kernel.The fact that not all DPPs are L-ensembles is unfortunate, but t...
• STRONG APPROXIMATION OF GAUSSIAN ? ENSEMBLE CHARACTERISTIC POLYNOMIALS: THE HYPERBOLIC REGIME AI翻译
  作者：Lambert, Gaultier; Paquette, Elliot
  作者单位：University of Zurich; McGill University
  摘要：We investigate the characteristic polynomials phi N of the Gaussian beta ensemble for general beta > 0 through its transfer matrix recurrence. Our motivation is to obtain a (probabilistic) approximation for phi N in terms of a Gaussian log-correlated field. We distinguish between different types of transfer matrices and analyze completely the hyperbolic part of the recurrence. As a result, we obtain a new coupling between phi N and a Gaussian analytic function with an error which is uniform aw...
• DIRECTED POLYMER FOR VERY HEAVY TAILED RANDOM WALKS AI翻译
  作者：Viveros, Roberto
  摘要：In the present work, we investigate the case of directed polymer in a random environment (DPRE), when the increments of the one-dimensional random walk are heavy-tailed with tail-exponent equal to zero (P[|X1| >= n] decays slower than any power of n). This case has not yet been studied in the context of directed polymers and presents key differences with the simple symmetric random walk case and the cases where the increments belong to the domain of attraction of an alpha-stable law, where alp...
• CONVERGENCE OF A TIME-STEPPING SCHEME TO THE FREE BOUNDARY IN THE SUPERCOOLED STEFAN PROBLEM AI翻译
  作者：Kaushansky, Vadim; Reisinger, Christoph; Shkolnikov, Mykhaylo; Song, Zhuo Qun
  作者单位：University of California System; University of California Los Angeles; University of Oxford; Princeton University; Princeton University; Princeton University
  摘要：The supercooled Stefan problem and its variants describe the freezing of a supercooled liquid in physics, as well as the large system limits of sys-temic risk models in finance and of integrate-and-fire models in neuroscience. Adopting the physics terminology, the supercooled Stefan problem is known to feature a finite-time blow-up of the freezing rate for a wide range of initial temperature distributions in the liquid. Such a blow-up can result in a discon-tinuity of the liquid-solid boundary...
• ASYMPTOTICALLY LINEAR ITERATED FUNCTION SYSTEMS ON THE REAL LINE AI翻译
  作者：Alsmeyer, Gerold; Brofferio, Sara; Buraczewski, Dariusz
  作者单位：University of Munster; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; University of Wroclaw
  摘要：Given a sequence of i.i.d. random functions Psi(n) : R -> R, n is an element of N, we consider the iterated function system and Markov chain, which is recursively defined by X-0(x) := x and X-n(x) := Psi(n-1)(X-n-1(x)) for x is an element of R and n is an element of N. Under the two basic assumptions that the Psi(n) are a.s. continuous at any point in R and asymptotically linear at the endpoints +/-infinity, we study the tail behavior of the stationary laws of such Markov chains by means of Ma...