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作者：Graham, Carl
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS)
摘要：Regenerative properties of the linear Hawkes process are proved under minimal assumptions on the transfer function, which may have unbounded support. For this, an original construction of the Hawkes process as a functional of a Poisson point process is derived from the immigration-birth representation, and the independence properties of the Poisson point process are exploited to exhibit regeneration times which are anticipative and not even measurable w.r.t. the Hawkes process. The regeneratio...
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作者：Peigne, Marc; Woess, Wolfgang
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Orleans; Universite de Tours; Graz University of Technology
摘要：Let X = (X-1, X-2) be a two-dimensional random variable and X(n), n is an element of N, a sequence of i.i.d. copies of X. The associated random walk is S(n) = X(1)+ ... + X(n). The corresponding absorbed-reflected walk W(n), n is an element of N, in the first quadrant is given by W(0) = x is an element of R-+(2) and W(n) = max{0, W(n - 1) - X(n)}, where the maximum is taken coordinate-wise. This is often called the Lindley process and models the waiting times in a two-server queue. We characte...
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作者：Budhiraja, Amarjit; Friedlander, Eric; Wu, Ruoyu
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of Chicago; Iowa State University
摘要：The join-the-shortest-queue routing policy is studied in an asymptotic regime where the number of processors n scales with the arrival rate. A large deviation principle (LDP) for the occupancy process is established, as n -> infinity, in a suitable infinite-dimensional path space. Model features that present technical challenges include, Markovian dynamics with discontinuous statistics, a diminishing rate property of the transition probability rates, and an infinite-dimensional state space. Th...
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作者：Heiny, Johannes; Mikosch, Thomas; Yslas, Jorge
作者单位：Ruhr University Bochum; University of Copenhagen
摘要：We study point process convergence for sequences of i.i.d. random walks. The objective is to derive asymptotic theory for the extremes of these random walks. We show convergence of the maximum random walk to the Gumbel distribution under the existence of a (2 + delta)th moment. We make heavy use of precise large deviation results for sums of i.i.d. random variables. As a consequence, we derive the joint convergence of the off-diagonal entries in sample covariance and correlation matrices of a ...
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作者：Jaber, Eduardo Abi; Cuchiero, Christa; Larsson, Martin; Pulido, Sergio
作者单位：University of Vienna; Carnegie Mellon University; Ecole Nationale Superieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：We obtain general weak existence and stability results for stochastic convolution equations with jumps under mild regularity assumptions, allowing for non-Lipschitz coefficients and singular kernels. Our approach relies on weak convergence in L-p spaces. The main tools are new a priori estimates on Sobolev-Slobodeckij norms of the solution, as well as a novel martingale problem that is equivalent to the original equation. This leads to generic approximation and stability theorems in the spirit...
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作者：Jaramillo, Arturo; Nourdin, Ivan; Peccati, Giovanni
作者单位：University of Luxembourg
摘要：We consider empirical processes associated with high-frequency observations of a fractional Brownian motion (fBm) X with Hurst parameter H is an element of (0, 1), and derive conditions under which these processes verify a (possibly uniform) law of large numbers, as well as a second order (possibly uniform) limit theorem. We devote specific emphasis to the zero energy case, corresponding to a kernel whose integral on the real line equals zero. Our asymptotic results are associated with explici...
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作者：Natarovskii, Viacheslav; Rudolf, Daniel; Sprungk, Bjoern
作者单位：University of Gottingen; Technical University Freiberg
摘要：We prove Wasserstein contraction of simple slice sampling for approximate sampling w.r.t. distributions with log-concave and rotational invariant Lebesgue densities. This yields, in particular, an explicit quantitative lower bound of the spectral gap of simple slice sampling. Moreover, this lower bound carries over to more general target distributions depending only on the volume of the (super-)level sets of their unnormalized density.
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作者：Jourdain, Benjamin; Lelievre, Tony; Zitt, Pierre-Andre
作者单位：Inria; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：By drawing a parallel between metadynamics and self interacting models for polymers, we study the longtime convergence of the original metadynamics algorithm in the adiabatic setting, namely when the dynamics along the collective variables decouples from the dynamics along the other degrees of freedom. We also discuss the bias which is introduced when the adiabatic assumption does not hold.
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作者：Dario, Paul
作者单位：Tel Aviv University
摘要：We prove optimal quantitative estimates on the first-order correctors on supercritical percolation clusters: we show that they are bounded in dimension larger than 3 and have logarithmic growth in dimension 2 in the sense of stretched exponential moments. The main ingredients are a renormalization scheme of the supercritical percolation cluster, following the works of Pisztora (Probab. Theory Related Fields 104 (1996) 427-466); large-scale regularity estimates developed by Armstrong and the au...
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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...
