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作者：Villemonais, Denis; Watson, Alexander R.
作者单位：Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Institut Universitaire de France; University of London; University College London
摘要：In a growth-fragmentation system, cells grow in size slowly and split apart at random. Typically, the number of cells in the system grows exponentially and the distribution of the sizes of cells settles into an equilibrium asymptotic profile. In this work we introduce a new method to prove this asymptotic behaviour for the growth-fragmentation equation, and show that the convergence to the asymptotic profile occurs at exponential rate. We do this by identifying an associated sub-Markov process...
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作者：Zhang, Xuhui; Blanchet, Jose; Marzouk, Youssef; Nguyen, Viet Anh; Wang, Sven
作者单位：Stanford University; Massachusetts Institute of Technology (MIT); Chinese University of Hong Kong; Humboldt University of Berlin
摘要：We study a distributionally robust optimization formulation (i.e., a min-max game) for two representative problems in Bayesian nonparametric estimation: Gaussian process regression and, more generally, linear inverse problems. Our formulation seeks the best mean-squared error predictor in an infinite-dimensional space against an adversary who chooses the worst-case model in a Wasserstein ball around a nominal infinite-dimensional Bayesian model. The transport cost is chosen to control features...
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作者：Chen, Zaiwei; Maguluri, Siva Theja; Zubeldia, Martin
作者单位：Purdue University System; Purdue University; University System of Georgia; Georgia Institute of Technology; University of Minnesota System; University of Minnesota Twin Cities
摘要：In this paper, we establish maximal concentration bounds for the iterates generated by a stochastic approximation (SA) algorithm under a contractive operator with respect to some arbitrary norm (e.g., the pound infinity-norm). We consider two settings where the iterates are potentially unbounded: SA with bounded multiplicative noise and SA with sub-Gaussian additive noise. Our maximal concentration inequalities state that the convergence error has a sub-Gaussian tail in the additive noise sett...
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作者：Gerolla, Luca; Hairer, Martin; Li, Xue-Mei
作者单位：Imperial College London; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We study the large-scale dynamics of the solution to a nonlinear stochastic heat equation (SHE) in dimensions d >= 3 with long-range dependence. This equation is driven by multiplicative Gaussian noise, which is white in time and coloured in space with nonintegrable spatial covariance that decays at the rate of |x|-kappa at infinity, where kappa E (2, d). Inspired by recent studies on SHE and KPZ equations driven by noise with compactly supported spatial correlation, we demonstrate that the co...
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作者：Banas, L'Umbomir; Gess, Benjamin; Neuss, Marius
作者单位：University of Bielefeld; Max Planck Society; Deutsche Bundesbank
摘要：We study scaling limits of the weakly driven Zhang and the Bak- Tang-Wiesenfeld (BTW) model for self-organized criticality. We show that the weakly driven Zhang model converges to a stochastic partial differential equation (PDE) with singular-degenerate diffusion. In addition, the deterministic BTW model is shown to converge to a singular-degenerate PDE. Alternatively, the proof of the scaling limit can be understood as a convergence proof of a finite-difference discretization for singular-deg...
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作者：Khudiakova, Ksenia A.; Maas, Jan; Pedrotti, Francesco
作者单位：Institute of Science & Technology - Austria
摘要：We prove upper bounds on the L infinity-Wasserstein distance from optimal transport between strongly log-concave probability densities and logLipschitz perturbations. In the simplest setting, such a bound amounts to a transport-information inequality involving the L infinity-Wasserstein metric and the relative L infinity-Fisher information. We show that this inequality can be sharpened significantly in situations where the involved densities are anisotropic. Our proof is based on probabilistic...
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作者：Giles, Michael b.; Aji-ali, Abdul-lateef
作者单位：University of Oxford; Heriot Watt University; University of Edinburgh
摘要：We propose a new Monte Carlo-based estimator for digital options with assets modelled by a stochastic differential equation (SDE). The new estimator is based on repeated path splitting and relies on the correlation of approximate paths of the underlying SDE that share parts of a Brownian path. Combining this new estimator with multilevel Monte Carlo (MLMC) leads to an estimator with a computational complexity that is similar to the complexity of a MLMC estimator when applied to options with Li...
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作者：Kardaras, Constantinos
作者单位：University of London; London School Economics & Political Science
摘要：Stochastic integrals are defined with respect to a collection P = (P-i; i is an element of I) of continuous semimartingales, imposing no assumptions on the index set I and the subspace of R-I where P takes values. The integrals are constructed though finite-dimensional approximation, identifying the appropriate local geometry that allows extension to infinite dimensions. For local martingale integrators, the resulting space S(P) of stochastic integrals has an operational characterisation via a...
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作者：Goldfeld, Ziv; Kato, Kengo; Nietert, Sloan; Rioux, Gabriel
作者单位：Cornell University; Cornell University; Cornell University; Cornell University
摘要：The Wasserstein distance is a metric on a space of probability measures that has seen a surge of applications in statistics, machine learning, and applied mathematics. However, statistical aspects of Wasserstein distances are bottlenecked by the curse of dimensionality, whereby the number of data points needed to accurately estimate them grows exponentially with dimension. Gaussian smoothing was recently introduced as a means to alleviate the curse of dimensionality, giving rise to a parametri...
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作者：Jourdain, Benjamin; Menozzi, Stephane
作者单位：Inria; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite Paris Saclay
摘要：We are interested in the time discretization of stochastic differential equations with additive d-dimensional Brownian noise and L-q - L-rho drift coefficient when the condition d/rho + 2/q < 1, under which Krylov and Rockner (Probab. Theory Related Fields 131 (2005) 154-196) proved existence of a unique strong solution, is met. We show weak convergence with order 1/2 (1 - (d/rho + 2/q)) which corresponds to half the distance to the threshold for the Euler scheme with randomized time variable ...
