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作者：Touboul, Jonathan
作者单位：Universite PSL; College de France
摘要：We consider the problem of the limit of bio-inspired spatially extended neuronal networks including an infinite number of neuronal types (space locations), with space-dependent propagation delays modeling neural fields. The propagation of chaos property is proved in this setting under mild assumptions on the neuronal dynamics, valid for most models used in neuroscience, in a mesoscopic limit, the neural-field limit, in which we can resolve the quite fine structure of the neuron's activity in s...
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作者：Butkovsky, Oleg
作者单位：Lomonosov Moscow State University; Technion Israel Institute of Technology
摘要：We establish subgeometric bounds on convergence rate of general Markov processes in the Wasserstein metric. In the discrete time setting we prove that the Lyapunov drift condition and the existence of a good d-small set imply subgeometric convergence to the invariant measure. In the continuous time setting we obtain the same convergence rate provided that there exists a good d-small set and the Douc-Fort-Guillin supermaffingale condition holds. As an application of our results, we prove that t...
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作者：Galichon, A.; Henry-Labordere, P.; Touzi, N.
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris
摘要：We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade European call options for all possible strikes with some given maturity. This problem is classically approached by means of the Skorohod Embedding Problem (SEP). Instead, we provide a dual formulation which converts the superhedging problem into a continuous martingale optimal transportation problem. We then show that this formulation allo...
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作者：Khandwawala, Mustafa; Sundaresan, Rajesh
作者单位：Indian Institute of Science (IISC) - Bangalore
摘要：We apply the objective method of Aldous to the problem of finding the minimum-cost edge cover of the complete graph with random independent and identically distributed edge costs. The limit, as the number of vertices goes to infinity, of the expected minimum cost for this problem is known via a combinatorial approach of Hessler and Wastlund. We provide a proof of this result using the machinery of the objective method and local weak convergence, which was used to prove the (2) limit of the ran...
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作者：Pal, Soumik d; Shkolnikov, Mykhaylo
作者单位：University of Washington; University of Washington Seattle; University of California System; University of California Berkeley
摘要：We consider a finite or countable collection of one-dimensional Brownian particles whose dynamics at any point in time is determined by their rank in the entire particle system. Using transportation cost inequalities for stochastic processes we provide uniform fluctuation bounds for the ordered particles, their local time of collisions and various associated statistics over intervals of time. For example, such processes, when exponentiated and rescaled, exhibit power law decay under stationari...
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作者：Larsson, Martin
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Swiss Finance Institute (SFI)
摘要：When a strict local martingale is projected onto a subfiltration to which it is not adapted, the local martingale property may be lost, and the finite variation part of the projection may have singular paths. This phenomenon has consequences for arbitrage theory in mathematical finance. In this paper it is shown that the loss of the local martingale property is related to a measure extension problem for the associated Follmer measure. When a solution exists, the finite variation part of the pr...
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作者：Collet, Pierre; Leonardi, Florencia
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP); Universidade de Sao Paulo
摘要：In this paper we prove that the asymptotic rate of exponential loss of memory of a finite state hidden Markov model is bounded above by the difference of the first two Lyapunov exponents of a certain product of matrices. We also show that this bound is in fact realized, namely for almost all realizations of the observed process we can find symbols where the asymptotic exponential rate of loss of memory attains the difference of the first two Lyapunov exponents. These results are derived in par...
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作者：Chafai, Djalil; Gozlan, Nathael; Zitt, Pierre-Andre
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Gustave-Eiffel
摘要：We study a physical system of N interacting particles in R-d, d >= 1, subject to pair repulsion and confined by an external field. We establish a large deviations principle for their empirical distribution as N tends to infinity. In the case of Riesz interaction, including Coulomb interaction in arbitrary dimension d > 2, the rate function is strictly convex and admits a unique minimum, the equilibrium measure, characterized via its potential. It follows that almost surely, the empirical distr...
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作者：Addario-Berry, Louigi; Broutin, Nicolas; Holmgren, Cecilia
作者单位：McGill University; Stockholm University
摘要：We provide simplified proofs for the asymptotic distribution of the number of cuts required to cut down a Galton-Watson tree with critical, finite-variance offspring distribution, conditioned to have total progeny n. Our proof is based on a coupling which yields a precise, nonasymptotic distributional result for the case of uniformly random rooted labeled trees (or, equivalently, Poisson Galton-Watson trees conditioned on their size). Our approach also provides a new, random reversible transfo...
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作者：Dieker, A. B.; Gao, X.
作者单位：University System of Georgia; Georgia Institute of Technology; Chinese University of Hong Kong
摘要：This paper studies diffusion processes constrained to the positive orthant under infinitesimal changes in the drift. Our first main result states that any constrained function and its (left) drift-derivative is the unique solution to an augmented Skorohod problem. Our second main result uses this characterization to establish a basic adjoint relationship for the stationary distribution of the constrained diffusion process jointly with its left-derivative process.
