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作者：Norris, James
作者单位：University of Cambridge
摘要：An explicit estimate is derived for Kac's mean-field model of colliding hard spheres, which compares, in a Wasserstein distance, the empirical velocity distributions for two versions of the model based on different numbers of particles. For suitable initial data, with high probability, the two processes agree to within a tolerance of order N-1/d, where N is the smaller particle number and d is the dimension, provided that d >= 3. From this estimate we can deduce that the spatially homogeneous ...
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作者：Frikha, Noufel
作者单位：Universite Paris Cite
摘要：This paper studies multi-level stochastic approximation algorithms. Our aim is to extend the scope of the multi-level Monte Carlo method recently introduced by Giles [Oper. Res. 56 (2008) 607-617] to the framework of stochastic optimization by means of stochastic approximation algorithm. We first introduce and study a two-level method, also referred as statistical Romberg stochastic approximation algorithm. Then its extension to a multi-level method is proposed. We prove a central limit theore...
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作者：Madaule, Thomas; Rhodes, Remi; Vargas, Vincent
作者单位：Universite Paris 13; Universite PSL; Universite Paris-Dauphine; Universite PSL; Ecole Normale Superieure (ENS)
摘要：In this paper, we consider the Gibbs measure associated to a logarithmically correlated random potential (including two-dimensional free fields) at low temperature. We prove that the energy landscape freezes and enters in the so-called glassy phase. The limiting Gibbs weights are integrated atomic random measures with random intensity expressed in terms of the critical Gaussian multiplicative chaos constructed in [Ann. Probab. 42 (2014) 1769-1808 and Comm. Math. Phys. (2013) To appear]. This c...
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作者：Bayraktar, Erhan; Li, Jiaqi
作者单位：University of Michigan System; University of Michigan
摘要：We extend the stochastic Perron method to analyze the framework of stochastic target games, in which one player tries to find a strategy such that the state process almost surely reaches a given target no matter which action is chosen by the other player. Within this framework, our method produces a viscosity sub-solution (super-solution) of a Hamilton-Jacobi-Bellman (HJB) equation. We then characterize the value function as a viscosity solution to the HJB equation using a comparison result an...
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作者：Cortez, Roberto; Fontbona, Joaquin
作者单位：Universidad de Chile; Universidad de Chile
摘要：We study a class of one-dimensional particle systems with true (Bird type) binary interactions, which includes Kac's model of the Boltzmann equation and nonlinear equations for the evolution of wealth distribution arising in kinetic economic models. We obtain explicit rates of convergence for the Wasserstein distance between the law of the particles and their limiting law, which are linear in time and depend in a mild polynomial manner on the number of particles. The proof is based on a novel ...
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作者：Choukroun, Sebastien; Cosso, Andrea
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite
摘要：We are interested in stochastic control problems coming from mathematical finance and, in particular, related to model uncertainty, where the uncertainty affects both volatility and intensity. This kind of stochastic control problem is associated to a fully nonlinear integro-partial differential equation, which has the peculiarity that the measure (lambda(a, .))a characterizing the jump part is not fixed but depends on a parameter a which lives in a compact set A of some Euclidean space R-q. W...
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作者：Cox, J. Theodore; Peres, Yuval; Steif, Jeffrey E.
作者单位：Syracuse University; Microsoft; Chalmers University of Technology; University of Gothenburg
摘要：Given a continuous time Markov Chain {q (x, y)} on a finite set S, the associated noisy voter model is the continuous time Markov chain on {0, 1}(S), which evolves in the following way: (1) for each two sites x and y in S, the state at site x changes to the value of the state at site y at rate q (x, y); (2) each site rerandomizes its state at rate 1. We show that if there is a uniform bound on the rates {q (x, y)} and the corresponding stationary distributions are almost uniform, then the mixi...
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作者：Crane, Harry
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：We study a broad class of stochastic process models for dynamic networks that satisfy the minimal regularity conditions of (i) exchangeability and (ii) cadlag sample paths. Our main theorems characterize these processes through their induced behavior in the space of graph limits. Under the assumption of time-homogeneous Markovian dependence, we classify the dis-continuities of these processes into three types, prove bounded variation of the sample paths in graph limit space and express the pro...
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作者：Blath, Jochen; Casanova, Adrian Gonzalez; Kurt, Noemi; Wilke-Berenguer, Maite
作者单位：Technical University of Berlin
摘要：We identify a new natural coalescent structure, which we call the seed bank coalescent, that describes the gene genealogy of populations under the influence of a strong seed-bank effect, where dormant forms of individuals (such as seeds or spores) may jump a significant number of generations before joining the active population. Mathematically, our seed-bank coalescent appears as scaling limit in a Wright-Fisher model with geometric seed-bank age structure if the average time of seed dormancy ...
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作者：Kramkov, Dmitry; Pulido, Sergio
作者单位：Carnegie Mellon University; Universite Paris Saclay; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider a financial model where the prices of risky assets are quoted by a representative market maker who takes into account an exogenous demand. We characterize these prices in terms of a system of BSDEs with quadratic growth. We show that this system admits a unique solution for every bounded demand if and only if the market maker's risk-aversion is sufficiently small. The uniqueness is established in the natural class of solutions, without any additional norm restrictions. To the best ...
