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作者：Khoshnevisan, Davar; Kim, Kunwoo; Mueller, Carl
作者单位：Utah System of Higher Education; University of Utah; Pohang University of Science & Technology (POSTECH); University of Rochester
摘要：We consider a generalization of the parabolic Anderson model driven by space-time white noise, also called the stochastic heat equation, on the real line: partial derivative(t) u(t, x) = 1/2 partial derivative(2)(x)u(t, x) + sigma(u(t, x)xi(t, x) for t > 0 and x is an element of R. High peaks of solutions have been extensively studied under the name of intermittency, but less is known about spatial regions between peaks, which we may loosely refer to as valleys. We present two results about th...
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作者：Sadhu, Ritwik; Goldfeld, Ziv; Kato, Kengo
作者单位：Cornell University; Cornell University
摘要：We study statistical inference for the optimal transport (OT) map (also known as the Brenier map) from a known absolutely continuous reference distribution onto an unknown finitely discrete target distribution. We derive limit distributions for the Lp-error with arbitrary p E [1, oc) and for linear functionals of the empirical OT map, together with their moment convergence. The former has a non-Gaussian limit, whose explicit density is derived, while the latter attains asymptotic normality. Fo...
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作者：Koehler, Frederic; Mossel, Elchanan
作者单位：University of Chicago; University of Chicago; Massachusetts Institute of Technology (MIT)
摘要：Arrow's theorem concerns a fundamental problem in social choice theory: given the individual preferences of members of a group, how can they be aggregated to form rational group preferences? Arrow showed that in an election between three or more candidates, there are situations where any voting rule satisfying a small list of natural fairness axioms must produce an apparently irrational intransitive outcome. Furthermore, quantitative versions of Arrow's theorem in the literature show that when...
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作者：Xu, Wei
作者单位：Beijing Institute of Technology
摘要：In this work, several convergence results are established for nearly critical self-excited systems in which event arrivals are described by multivariate marked Hawkes point processes. Under some mild high -frequency assumptions, the rescaled density process behaves asymptotically like a multi -type continuous -state branching process with immigration, which is the unique solution to a multi -dimensional stochastic differential equation with dynamical mechanism similar to that of multivariate H...
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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...
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作者：Bayraktar, Erhan; Yao, Song
作者单位：University of Michigan System; University of Michigan; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
摘要：We analyze an optimal stopping problem with a series of inequality-type and equality-type expectation constraints in a general non-Markovian framework. We show that the optimal stopping problem with expectation constraints (OSEC) in an arbitrary probability setting is equivalent to the constrained problem in weak formulation (an optimization over joint laws of stopping rules with Brownian motion and state dynamics on an enlarged canonical space), and thus the OSEC value is independent of a spe...
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作者：Bou-Rabee, Ahmed
作者单位：University of Chicago
摘要：We study scaling limits of exploding Abelian sandpiles using ideas from percolation and front propagation in random media. We establish sufficient conditions under which a limit shape exists and show via a family of counter-examples that convergence may not occur in general. A corollary of our proof is a simple criterion for determining if a sandpile is explosive; this strengthens a result of Fey, Levine and Peres (J. Stat. Phys. (2010) 138 143-159).
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作者：Ertel, Sebastian W.; Stannat, Wilhelm
作者单位：Technical University of Berlin
摘要：Ensemble Kalman-Bucy filters (EnKBFs) are an important tool in data assimilation that aim to approximate the posterior distribution for continuous time filtering problems using an ensemble of interacting particles. In this work we extend a previously derived unifying framework for consistent representations of the posterior distribution to correlated observation noise and use these representations to derive an EnKBF suitable for this setting as a constant gain approximation of these optimal fi...
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作者：Dubach, Guillaume
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We present general links between statistics of non-Hermitian random matrices and the distribution of the number of cycles of some specific random permutations. In particular, we derive explicit formulas for the generating functions of the number of cycles in the commutator [ sigma, tau] ] = sigma tau sigma (- 1 )tau (- 1) where sigma is uniformly distributed, and tau is either one cycle, the product of many transpositions, or the product of two cycles of same size, the latter case being a new ...
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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...
