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作者：Guo, Ivan; Loeper, Gregoire
作者单位：Monash University; Monash University
摘要：In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent constraints. Duality results are established, representing the solution in terms of path dependent partial differential equations (PPDEs). Moreover, we provide a dimension reduction result based on the new notion of semifiltrations, which identifies appropriate Markov...
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作者：Olvera-Cravioto, Mariana
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：The focus of this work is the asymptotic analysis of the tail distribution of Google's PageRank algorithm on large scale-free directed networks. In particular, the main theorem provides the convergence, in the Kantorovich-Rubinstein metric, of the rank of a randomly chosen vertex in graphs generated via either a directed configuration model or an inhomogeneous random digraph. The theorem fully characterizes the limiting distribution by expressing it as a random sum of i.i.d. copies of the attr...
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作者：Atar, Rami; Budhiraja, Amarjit; Dupuis, Paul; Wu, Ruoyu
作者单位：Technion Israel Institute of Technology; University of North Carolina; University of North Carolina Chapel Hill; Brown University; Iowa State University
摘要：This paper develops tools to obtain robust probabilistic estimates for queueing models at the large deviations (LD) scale. These tools are based on the recently introduced robust Renyi bounds, which provide LD estimates (and more generally risk-sensitive (RS) cost estimates) that hold uniformly over an uncertainty class of models, provided that the class is defined in terms of Renyi divergence with respect to a reference model and that estimates are available for the reference model. One very ...
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作者：Caillerie, Nils; Vovelle, Julien
作者单位：Georgetown University; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We derive the hydrodynamic limit of a kinetic equation with a stochastic, short range perturbation of the velocity operator. Under some mixing hypotheses on the stochastic perturbation, we establish a diffusion-approximation result: the limit we obtain is a parabolic stochastic partial differential equation on the macroscopic parameter, the density here.
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作者：Bender, Christian; Schweizer, Nikolaus
作者单位：Saarland University; Tilburg University
摘要：We propose a new least-squares Monte Carlo algorithm for the approximation of conditional expectations in the presence of stochastic derivative weights. The algorithm can serve as a building block for solving dynamic programming equations, which arise, for example, in nonlinear option pricing problems or in probabilistic discretization schemes for fully nonlinear parabolic partial differential equations. Our algorithm can be generically applied when the underlying dynamics stem from an Euler a...
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作者：Szpruch, Lukasz; Tse, Alvin
作者单位：University of Edinburgh
摘要：Let mu is an element of P-2(R-d), where P-2(R-d) denotes the space of square integrable probability measures, and consider a Borel-measurable function Phi : P-2(R-d) -> R. In this paper we develop an antithetic Monte Carlo estimator (A-MLMC) for Phi(mu), which achieves sharp error bound under mild regularity assumptions. The estimator takes as input the empirical laws mu(N) = 1/N Sigma(N)(i =1) delta X-i, where (a) (X-i)(i =1)(N) is a sequence of i.i.d. samples from mu or (b) (X-i)(i =1)(N) is...
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作者：Kroshnin, Alexey; Spokoiny, Vladimir; Suvorikova, Alexandra
作者单位：Russian Academy of Sciences; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：In this work we introduce the concept of Bures-Wasserstein barycenter Q(*), that is essentially a Frechet mean of some distribution P supported on a subspace of positive semi-definite d-dimensional Hermitian operators H+(d). We allow a barycenter to be constrained to some affine subspace of H+(d), and we provide conditions ensuring its existence and uniqueness. We also investigate convergence and concentration properties of an empirical counterpart of Q(*) in both Frobenius norm and Bures-Wass...
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作者：Rockner, Michael; Yang, Huanyu; Zhu, Rongchan
作者单位：University of Bielefeld; Free University of Berlin; Beijing Institute of Technology
摘要：We consider the stochastic two-dimensional Cahn-Hilliard equation which is driven by the derivative in space of a space-time white noise. We use two different approaches to study this equation. First we prove that there exists a unique solution Y to the shifted equation (1.4). Then X := Y + Z is the unique solution to the stochastic Cahn-Hilliard equation, where Z is the corresponding O-U process. Moreover, we use the Dirichlet form approach in (Probab. Theory Related Fields 89 (1991) 347-386)...
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作者：Gamarnik, David; Kizildag, Eren C.
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：We establish the average-case hardness of the algorithmic problem of exact computation of the partition function associated with the Sherrington-Kirkpatrick model of spin glasses with Gaussian couplings and random external field. In particular, we establish that unless P = #P, there does not exist a polynomial-time algorithm to exactly compute the partition function on average. This is done by showing that if there exists a polynomial time algorithm, which exactly computes the partition functi...
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作者：Matoussi, Anis; Possamai, Dylan; Zhou, Chao
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Le Mans Universite; Swiss Federal Institutes of Technology Domain; ETH Zurich; National University of Singapore
摘要：The aim of this short note is to fill in a gap in our earlier paper (Ann. Appl. Probab. 23 (2013) 2420-2457) on 2BSDEs with reflections, and to explain how to correct the subsequent results in the second paper (Stochastic Process. Appl. 124 (2014) 2281-2321). We also provide more insight on the properties of 2RBSDEs, in the light of the recent contributions (Li and Peng (2017); Soumana Hima (2017)) in the so-called G-framework.
