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作者：Baurdoux, Erik J.; Pedraza, Jose M.
作者单位：University of London; London School Economics & Political Science; University of Manchester
摘要：Given a spectrally negative Levy process X drifting to infinity, (inspired on the early ideas of Shiryaev (2002)) we are interested in finding a stopping time that minimises the Lp distance (p > 1) with g, the last time X is negative. The solution is substantially more difficult compared to the case p = 1, for which it was shown by Baurdoux and Pedraza (2020) that it is optimal to stop as soon as X exceeds a constant barrier. In the case of p > 1 treated here, we prove that solving this optima...
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作者：Erignoux, Clement; Simon, Marielle; Zhao, Linjie
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lille; Inria; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Huazhong University of Science & Technology
摘要：We derive the hydrodynamic limit for two degenerate lattice gases, the facilitated exclusion process (FEP) and the facilitated zero-range process (FZRP), both in the symmetric and the asymmetric case. For both processes, the hydrodynamic limit in the symmetric case takes the form of a diffusive Stefan problem, whereas the asymmetric case is characterized by a hyperbolic Stefan problem. Although the FZRP is attractive, a property that we extensively use to derive its hydrodynamic limits in both...
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作者：Hening, Alexandru; Qi, Weiwei; Shen, Zhongwei; Yi, Yingfei
作者单位：Texas A&M University System; Texas A&M University Kingsville; University of Alberta
摘要：The present paper is devoted to the study of the long term dynamics of diffusion processes modelling a single species that experiences both demographic and environmental stochasticity. In our setting, the long term dynamics of the diffusion process in the absence of demographic stochasticity is determined by the sign of Lambda(0), the external Lyapunov exponent, as follows: Lambda(0 )< 0 implies (asymptotic) extinction and Lambda(0 )> 0 implies convergence to a unique positive stationary distr...
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作者：Itkin, David; Larsson, Martin
作者单位：Imperial College London; Carnegie Mellon University
摘要：We propose a unified approach to several problems in stochastic portfolio theory (SPT), which is a framework for equity markets with a large number d of stocks. Our approach combines open markets , where trading is confined to the top N capitalized stocks as well as the market portfolio consisting of all d assets, with a parametric family of models which we call hybrid Jacobi processes . We provide a detailed analysis of ergodicity, particle collisions, and boundary attainment, and use these r...
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作者：Bresler, Guy; Nagaraj, Dheeraj; Nichani, Eshaan
作者单位：Massachusetts Institute of Technology (MIT); Alphabet Inc.; Google Incorporated; Princeton University
摘要：In this paper, we consider the problem of sampling from the low temperature exponential random graph model (ERGM). The usual approach is via Markov chain Monte Carlo, but Bhamidi et al. showed that any local Markov chain suffers from an exponentially large mixing time due to metastable states. We instead consider metastable mixing, a notion of approximate mixing relative to the stationary distribution, for which it turns out to suffice to mix only within a collection of metastable states. We s...
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作者：Brueckerhoff, Martin; Huesmann, Martin
作者单位：University of Munster
摘要：In this article, we show an intimate connection between two objects in probability theory, which received some attention in the last years: shadows of measures and barrier solutions to the Skorokhod embedding problem (SEP). The shadow of a measure mu in the measure. is the key object in the construction of the left-curtain coupling and its siblings in martingale optimal transport by Beiglbock and Juillet (Ann. Probab. 44 (2016) 42-106; Trans. Amer. Math. Soc. 374 (2021) 4973-5002). Many promin...
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作者：Eckstein, Stephan; Pammer, Gudmund
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Adapted optimal transport (AOT) problems are optimal transport problems for distributions of a time series where couplings are constrained to have a temporal causal structure. In this paper, we develop computational tools for solving AOT problems numerically. First, we show that AOT problems are stable with respect to perturbations in the marginals, and thus arbitrary AOT problems can be approximated by sequences of linear programs. We further study entropic methods to solve AOT problems. We s...
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作者：Bristiel, Alexandre; Salez, Justin
作者单位：Universite PSL; Universite Paris-Dauphine; Universite PSL
摘要：We consider activated random walks on arbitrary finite networks, with particles being inserted at random and absorbed at the boundary. Despite the nonreversibility of the dynamics and the lack of knowledge on the stationary distribution, we explicitly determine the relaxation time of the process, and prove that separation cutoff is equivalent to the product condition. We also provide sharp estimates on the center and width of the cutoff window. Finally, we illustrate those results by establish...
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作者：Hong, Minhao; Liu, Heguang; Xu, Fangjun
作者单位：Shanghai Maritime University; East China Normal University; East China Normal University
摘要：Under certain mild conditions, limit theorems for additive functionals of some d-dimensional self-similar Gaussian processes are obtained. These limit theorems work for general Gaussian processes including fractional Brownian motions, subfractional Brownian motions and bi-fractional Brownian motions. To prove these results, we use the method of moments and an enhanced chaining argument. The Gaussian processes under consideration are required to satisfy certain strong local nondeterminism prope...
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作者：Bianchi, Alessandra; Collet, Francesca; Magnanini, Elena
作者单位：University of Padua; University of Verona; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together with a complete characterization of the phase diagram of the model. We borrow tools from statistical mechanics to obtain limit theorems for the edge density. First, we investigate the asymptotic distribution of this quantity, as the graph size tends to infin...
