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作者：Bhattacharya, Sohom; Deb, Nabarun; Mukherjee, Sumit
作者单位：State University System of Florida; University of Florida; University of Chicago; Columbia University
摘要：In this paper we derive a large deviation principle (LDP) for inhomogeneous U/V-statistics of a general order. Using this, we derive a LDP for two types of statistics: random multilinear forms, and number of monochromatic copies of a subgraph. We show that the corresponding rate functions in these cases can be expressed as a variational problem over a suitable space of functions. We use the tools developed to study Gibbs measures with the corresponding Hamiltonians, which include tensor genera...
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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...
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作者：Jackson, Joe
作者单位：University of Texas System; University of Texas Austin
摘要：Using probabilistic methods, we establish a priori estimates for two classes of quasilinear parabolic systems of partial differential equations (PDEs). We treat in particular the case of a nonlinearity, which has quadratic growth in the gradient of the unknown. As a result of our estimates, we obtain the existence of classical solutions of the PDE system. From this, we infer the existence of solutions to a corresponding class of forward backward stochastic differential equations.
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作者：Han, Fang; Huang, Zhihan
作者单位：University of Washington; University of Washington Seattle; University of Pennsylvania
摘要：In their seminal work, Azadkia and Chatterjee ( Ann. Statist. 49 (2021) 3070-3102) initiated graph-based methods for measuring variable dependence strength. By appealing to nearest neighbor graphs based on the Euclidean metric, they gave an elegant solution to a problem of R & eacute;nyi ( Acta Math. Acad. Sci. Hung. 10 (1959) 441-451). This idea was later developed in Deb, Ghosal and Sen (2020) (https://arxiv.org/abs/2010.01768) and the authors there proved that, quite interestingly, Azadkia ...
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作者：Alon, Noga; Gunby, Benjamin; He, Xiaoyu; Shmaya, Eran; Solan, Eilon
作者单位：Princeton University; Rutgers University System; Rutgers University New Brunswick; State University of New York (SUNY) System; Stony Brook University; Tel Aviv University
摘要：A group of players are supposed to follow a prescribed profile of strategies. If they follow this profile, they will reach a given target. We show that if the target is not reached because some player deviates, then an outside observer can identify the deviator. We also construct identification methods in two nontrivial cases.
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作者：Deb, Nabarun; Mukherjee, Rajarshi; Mukherjee, Sumit; Yuan, Ming
作者单位：Columbia University; Harvard University
摘要：In this paper we study the effect of dependence on detecting a class of signals in Ising models, where the signals are present in a structured way. Examples include Ising models on lattices, and mean-field type Ising models (Erdos-Renyi, Random regular, and dense graphs). Our results rely on correlation decay and mixing type behavior for Ising models, and demonstrate the beneficial behavior of criticality in detection of strictly lower signals. As a by-product of our proof technique, we develo...
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作者：Avena, Luca; Capannol, Federico; Hazra, Rajat subhra; Quattropani, Matteo
作者单位：University of Florence; Leiden University - Excl LUMC; Leiden University; Sapienza University Rome
摘要：We consider the so-called directed configuration model (DCM), that is, a random directed graph with prescribed in- and out-degrees. In this random geometry, we study the meeting time of two random walks starting at stationarity, the coalescence time for a system of coalescent random walks, and the consensus time of the classical voter model. Indeed, it is known that the latter three quantities are related to each other under certain mean field conditions requiring fast enough mixing time and n...
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作者：Jacod, Jean; Lin, Huidi; Todorov, Viktor
作者单位：Sorbonne Universite; Universite Paris Cite; Northwestern University
摘要：In this paper we develop tests for detecting systematic jumps in asset prices of general form, including ones not explained by observable factors, and we further propose nonparametric estimates for them. The inference is based on a panel of high-frequency asset returns, with both the sampling frequency and the size of the cross-section increasing asymptotically. The feasible limit theory developed in the paper utilizes the different asymptotic roles played by diffusive versus jump risks and sy...
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作者：Prodhomme, A. drien; Strickler, Edouard
作者单位：Universite de Tours; Universite de Lorraine; Inria; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider an epidemic SIS model described by a multitype birth-and-death process in a randomly switching environment. That is, the infection and cure rates of the process depend on the state of a finite Markov jump process (the environment), whose transitions also depend on the number of infectives. The total size of the population is constant and equal to some K is an element of N*, and the number of infectives vanishes almost surely in finite time. We prove that, as K -> infinity, the proc...
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作者：Stannat, Wilhelm; Wessels, Lukas
作者单位：Technical University of Berlin; University System of Georgia; Georgia Institute of Technology
摘要：Using a recently introduced representation of the second order adjoint state as the solution of a function-valued backward stochastic partial differential equation (SPDE), we calculate the viscosity super- and subdifferential of the value function evaluated along an optimal trajectory for controlled semilinear SPDEs. This establishes the well-known connection between Pontryagin's maximum principle and dynamic programming within the framework of viscosity solutions. As a corollary, we derive th...
