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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 ...
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作者：Dimitrov, Evgeni; Murthy, Anushka
作者单位：University of South Carolina System; University of South Carolina Columbia; Stanford University
摘要：We consider the asymmetric simple exclusion process (ASEP) with half-flat initial condition. We show that the one-point marginals of the ASEP height function are described by those of the Airy(2 -> 1) process, introduced by Borodin-Ferrari-Sasamoto in (Comm. Pure Appl. Math. 61 (2008) 1603-1629). This result was conjectured by Ortmann-Quastel-Remenik (Ann. Appl. Probab. 26 (2016) 507-548), based on an informal asymptotic analysis of exact formulas for generating functions of the half-flat ASEP...
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作者：Khoshnevisan, Davar; Kim, Kunwoo; Mueller, Carl
作者单位：Utah System of Higher Education; University of Utah; Pohang University of Science & Technology (POSTECH); University of Rochester
摘要：We consider a generalization of the parabolic Anderson model driven by space-time white noise, also called the stochastic heat equation, on the real line: partial derivative(t) u(t, x) = 1/2 partial derivative(2)(x)u(t, x) + sigma(u(t, x)xi(t, x) for t > 0 and x is an element of R. High peaks of solutions have been extensively studied under the name of intermittency, but less is known about spatial regions between peaks, which we may loosely refer to as valleys. We present two results about th...
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作者：Bayraktar, Erhan; Yao, Song
作者单位：University of Michigan System; University of Michigan; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
摘要：We analyze an optimal stopping problem with a series of inequality-type and equality-type expectation constraints in a general non-Markovian framework. We show that the optimal stopping problem with expectation constraints (OSEC) in an arbitrary probability setting is equivalent to the constrained problem in weak formulation (an optimization over joint laws of stopping rules with Brownian motion and state dynamics on an enlarged canonical space), and thus the OSEC value is independent of a spe...
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作者：Ertel, Sebastian W.; Stannat, Wilhelm
作者单位：Technical University of Berlin
摘要：Ensemble Kalman-Bucy filters (EnKBFs) are an important tool in data assimilation that aim to approximate the posterior distribution for continuous time filtering problems using an ensemble of interacting particles. In this work we extend a previously derived unifying framework for consistent representations of the posterior distribution to correlated observation noise and use these representations to derive an EnKBF suitable for this setting as a constant gain approximation of these optimal fi...
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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：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：Emilia Caballero, Maria; Gonzalez Casanov, Adrian; Perez, Jose-Luis
作者单位：Universidad Nacional Autonoma de Mexico
摘要：When two (possibly different in distribution) continuous-state branching processes with immigration are present, we study the relative frequency of one of them when the total mass is forced to be constant at a dense set of times. This leads to a SDE whose unique strong solution will be the definition of a Lambda-asymmetric frequency process (Lambda-AFP). We prove that it is a Feller process and we calculate a large population limit when the total mass tends to infinity. This allows us to study...
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作者：Goldenshluger, Alexander; Jacobovic, Royi
作者单位：University of Haifa
摘要：Suppose that particles are randomly distributed in R-d, and they are subject to identical stochastic motion independently of each other. The Smoluchowski process describes fluctuations of the number of particles in an observation region over time. This paper studies properties of the Smoluchowski processes and considers related statistical problems. In the first part of the paper we revisit probabilistic properties of the Smoluchowski process in a unified and principled way: explicit formulas ...
