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作者：Berger, Quentin; Torri, Niccolo
作者单位：Sorbonne Universite
摘要：We introduce a natural generalization of Hammersley's Last-Passage Percolation (LPP) called Entropy-controlled Last-Passage Percolation (E-LPP), where points can be collected by paths with a global (path-entropy) constraint which takes into account the whole structure of the path, instead of a local (1-Lipschitz) constraint as in Hammersley's LPP. Our main result is to prove quantitative tail estimates on the maximal number of points that can be collected by a path with entropy bounded by a pr...
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作者：dos Reis, Goncalo; Salkeld, William; Tugaut, Julian
作者单位：University of Edinburgh; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：We show two Freidlin-Wentzell-type Large Deviations Principles (LDP) in path space topologies (uniform and Holder) for the solution process of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) using techniques which directly address the presence of the law in the coefficients and altogether avoiding decoupling arguments or limits of particle systems. We provide existence and uniqueness results along with several properties for a class of MV-SDEs having random coefficients and drifts of...
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作者：Gong, Ruoting; Mou, Chenchen; Swiech, Andrzej
作者单位：Illinois Institute of Technology; University of California System; University of California Los Angeles; University System of Georgia; Georgia Institute of Technology
摘要：We prove a stochastic representation formula for the viscosity solution of Dirichlet terminal-boundary value problem for a degenerate Hamilton- Jacobi-Bellman integro-partial differential equation in a bounded domain. We show that the unique viscosity solution is the value function of the associated stochastic optimal control problem. We also obtain the dynamic programming principle for the associated stochastic optimal control problem in a bounded domain.
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作者：Kliem, Sandra
作者单位：Goethe University Frankfurt
摘要：We consider the one-dimensional KPP-equation driven by space-time white noise. We show that for all parameters above the critical value for survival, there exist stochastic wavelike solutions which travel with a deterministic positive linear speed. We further give a sufficient condition on the initial condition of a solution to attain this speed. Our approach is in the spirit of corresponding results for the nearest-neighbor contact process respectively oriented percolation. Here, the main dif...
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作者：Chassagneux, Jean-Francois; Crisan, Dan; Delarue, Francois
作者单位：Universite Paris Cite; Imperial College London; Universite Cote d'Azur
摘要：This paper is dedicated to the presentation and the analysis of a numerical scheme for forward-backward SDEs of the McKean-Vlasov type, or equivalently for solutions to PDEs on the Wasserstein space. Because of the mean field structure of the equation, earlier methods for classical forward- backward systems fail. The scheme is based on a variation of the method of continuation. The principle is to implement recursively local Picard iterations on small time intervals. We establish a bound for t...
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作者：Bishop, A. N.; Del Moral, P.; Kamatani, K.; Remillard, B.
作者单位：University of Technology Sydney; Commonwealth Scientific & Industrial Research Organisation (CSIRO); Inria; Centre National de la Recherche Scientifique (CNRS); University of New South Wales Sydney; University of Osaka; Universite de Montreal; HEC Montreal
摘要：This article is concerned with the fluctuation analysis and the stability properties of a class of one-dimensional Riccati diffusions. These one-dimensional stochastic differential equations exhibit a quadratic drift function and a non-Lipschitz continuous diffusion function. We present a novel approach, combining tangent process techniques, Feynman-Kac path integration and exponential change of measures, to derive sharp exponential decays to equilibrium. We also provide uniform estimates with...
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作者：Barbour, A. D.; Rollin, Adrian
作者单位：University of Zurich; National University of Singapore
摘要：We prove a general normal approximation theorem for local graph statistics in the configuration model, together with an explicit bound on the error in the approximation with respect to the Wasserstein metric. Such statistics take the form T := Sigma(v is an element of V) H-v, where V is the vertex set, and H-v depends on a neighbourhood in the graph around v of size at most l. The error bound is expressed in terms of l, vertical bar V vertical bar, an almost sure bound on H-v, the maximum vert...
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作者：Muirhead, S.; Pymar, R.; dos Santos, R. S.
作者单位：University of London; King's College London; University of London; Birkbeck University London; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：The Bouchaud-Anderson model (BAM) is a generalisation of the parabolic Anderson model (PAM) in which the driving simple random walk is replaced by a random walk in an inhomogeneous trapping landscape; the BAM reduces to the PAM in the case of constant traps. In this paper, we study the BAM with double-exponential potential. We prove the complete localisation of the model whenever the distribution of the traps is unbounded. This may be contrasted with the case of constant traps (i.e., the PAM),...
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作者：Arapostathis, Ari; Pang, Guodong; Sandric, Nikola
作者单位：University of Texas System; University of Texas Austin; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of Zagreb
摘要：We study the ergodic properties of a class of multidimensional piecewise Ornstein-Uhlenbeck processes with jumps, which contains the limit of the queueing processes arising in multiclass many-server queues with heavy-tailed arrivals and/or asymptotically negligible service interruptions in the Halfin-Whitt regime as special cases. In these queueing models, the Ito equations have a piecewise linear drift, and are driven by either (1) a Brownian motion and a pure-jump Levy process, or (2) an ani...
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作者：Heydecker, Daniel
作者单位：University of Cambridge
摘要：We derive two estimates for the deviation of the N-particle, hard-spheres Kac process from the corresponding Boltzmann equation, measured in expected Wasserstein distance. Particular care is paid to the long-time properties of our estimates, exploiting the stability properties of the limiting Boltzmann equation at the level of realisations of the interacting particle system. As a consequence, we obtain an estimate for the propagation of chaos, uniformly in time and with polynomial rates, as so...
