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作者：DEL Moral, Pierre; Horton, Emma; Jasra, Ajay
作者单位：Inria; King Abdullah University of Science & Technology
摘要：The stability and contraction properties of positive integral semigroups on Polish spaces are investigated. Our novel analysis is based on the extension of V-norm contraction methods, associated to functionally weighted Banach spaces for Markov semigroups, to positive semigroups. This methodology is applied to a general class of positive and possibly time-inhomogeneous bounded integral semigroups and their normalised versions. The spectral theorems that we develop are an extension of Perron-Fr...
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作者：Han, Qiyang; Jiang, Tiefeng; Shen, Yandi
作者单位：Rutgers University System; Rutgers University New Brunswick; University of Minnesota System; University of Minnesota Twin Cities; University of Chicago
摘要：Le Cam's third/contiguity lemma is a fundamental probabilistic tool to compute the limiting distribution of a given statistic T-n under a nonnull sequence of probability measures {Q(n)}, provided its limiting distribution under a null sequence {P-n} is available, and the log likelihood ratio {log(dQ(n)/dP(n))} has a distributional limit. Despite its wide-spread applications to low-dimensional statistical problems, the stringent requirement of Le Cam's third/contiguity lemma on the distribution...
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作者：Hanin, Boris
作者单位：Princeton University
摘要：This article gives a new proof that fully connected neural networks with random weights and biases converge to Gaussian processes in the regime where the input dimension, output dimension, and depth are kept fixed, while the hidden layer widths tend to infinity. Unlike prior work, convergence is shown assuming only moment conditions for the distribution of weights and for quite general nonlinearities.
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作者：Johnston, Samuel G. G.; Kyprianou, Andreas; Rogers, Tim
作者单位：University of London; King's College London; University of Warwick; University of Bath
摘要：Consider a multitype coalescent process in which each block has a colour in {1, ... , d}. Individual blocks may change colour, and some number of blocks of various colours may merge to form a new block of some colour. We show that if the law of a multitype coalescent process is invariant under permutations of blocks of the same colour, has consistent Markovian projec-tions, and has asynchronous mergers, then it is a multitype A-coalescent: a process in which single blocks may change colour, tw...
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作者：Johnston, Samuel g. g.; Lambert, Amaury
作者单位：University of London; King's College London; Universite Paris Cite; Sorbonne Universite
摘要：We introduce a Poissonization method to study the coalescent structure of uniform samples from branching processes. This method relies on the simple observation that a uniform sample of size k taken from a random set with positive Lebesgue measure may be represented as a mixture of Poisson samples with rate lambda and mixing measure k d lambda/lambda. We develop a multitype analogue of this mixture representation, and use it to characterise the coalescent structure of multitype continuous-stat...
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作者：Wiesel, Johannes
作者单位：Carnegie Mellon University
摘要：We show continuity of the martingale optimal transport optimisation problem as a functional of its marginals. This is achieved via an estimate on the projection in the nested/causal Wasserstein distance of an arbitrary coupling on to the set of martingale couplings with the same marginals. As a corollary we obtain an independent proof of sufficiency of the monotonicity principle established in Beiglbock and Juillet (Ann. Probab. 44 (2016) 42- 106) for cost functions of polynomial growth.
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作者：Bose, Shreya; Ekren, Ibrahim
作者单位：State University System of Florida; Florida State University
摘要：We show that the problem of existence of equilibrium in Kyle's con-tinuous time insider trading model can be tackled by considering a forward -backward system coupled via an optimal transport type constraint at maturity. The forward component is a stochastic differential equation representing an endogenously determined state variable and the backward component is a quasilinear parabolic equation representing the pricing function. By obtain-ing a stochastic representation for the solution of su...
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作者：Puhalskii, Anatolii A.; Reed, Josh E.
作者单位：Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS; New York University
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作者：Delon, Julie; Gozlan, Nathael; SAINT Dizier, Alexandre
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
摘要：In this paper, we introduce a generalization of the Wasserstein barycenter, to a case where the initial probability measures live on different subspaces of R-d. We study the existence and uniqueness of this barycenter, we show how it is related to a larger multimarginal optimal transport problem, and we propose a dual formulation. Finally, we explain how to compute numerically this generalized barycenter on discrete distributions, and we propose an ex-plicit solution for Gaussian distributions.
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作者：Jara, Milton; Landim, Claudio
摘要：We prove that in dimension d <= 3 a modified density field of a stirring dynamics perturbed by a voter model converges to the stochastic heat equation.
