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作者：Cordero, Fernando; Hummel, Sebastian; Schertzer, Emmanuel
作者单位：University of Bielefeld; Sorbonne Universite; Universite Paris Cite
摘要：Lambda-Wright-Fisher processes provide a robust framework to describe the type-frequency evolution of an infinite neutral population. We add a polynomial drift to the corresponding stochastic differential equation to incorporate frequency-dependent selection. A decomposition of the drift allows us to approximate the solution of the stochastic differential equation by a sequence of Moran models. The genealogical structure underlying the Moran model leads in the large population limit to a gener...
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作者：Guillin, Arnaud; Liu, Wei; Wu, Liming; Zhang, Chaoen
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Clermont Auvergne (UCA); Wuhan University
摘要：In this paper we consider a mean field particle systems whose confinement potentials have many local minima. We establish some explicit and sharp estimates of the spectral gap and logarithmic Sobolev constants uniform in the number of particles. The uniform Poincare inequality is based on the work of Ledoux (In Seminaire de Probabilites, XXXV (2001) 167194, Springer) and the uniform logarithmic Sobolev inequality is based on Zegarlinski's theorem for Gibbs measures, both combined with an expli...
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作者：Dhara, Souvik; Sen, Subhabrata
作者单位：Massachusetts Institute of Technology (MIT); Harvard University
摘要：Consider the random graph sampled uniformly from the set of all simple graphs with a given degree sequence. Under mild conditions on the degrees, we establish a large deviation principle (LDP) for these random graphs, viewed as elements of the graphon space. As a corollary of our result, we obtain LDPs for functionals continuous with respect to the cut metric, and obtain an asymptotic enumeration formula for graphs with given degrees, subject to an additional constraint on the value of a conti...
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作者：Kallblad, Sigrid
作者单位：Royal Institute of Technology
摘要：We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales enables us to transform the distributional constraint into an initial condition and view the problem as a stochastic control problem; we establish the corresponding dynamic programming principle. The method offers a systematic approach for solving the problem for general constraints and under weak assumptions o...
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作者：De Angelis, Tiziano; Merkulov, Nikita; Palczewski, Jan
作者单位：University of Turin; University of Leeds
摘要：We prove that zero-sum Dynkin games in continuous time with partial and asymmetric information admit a value in randomised stopping times when the stopping payoffs of the players are general cadlag measurable processes. As a by-product of our method of proof we also obtain existence of optimal strategies for both players. The main novelties are that we do not assume a Markovian nature of the game nor a particular structure of the information available to the players. This allows us to go beyon...
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作者：Bouchard, Bruno; Tan, Xiaolu
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Chinese University of Hong Kong
摘要：We consider a general path-dependent version of the hedging problem with price impact of Bouchard et al. (SIAM J. Control Optim. 57 (2019) 4125-49), in which a dual formulation for the super-hedging price is obtained by means of PDE arguments, in a Markovian setting and under strong regularity conditions. Using only probabilistic arguments, we prove, in a path-dependent setting and under weak regularity conditions, that any solution to this dual problem actually allows one to construct explici...
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作者：Curato, Imma Valentina; Stelzer, Robert; Stroeh, Bennet
作者单位：Ulm University
摘要：We obtain central limit theorems for stationary random fields employing a novel measure of dependence called theta-lex weak dependence. We show that this dependence notion is more general than strong mixing, that is, it applies to a broader class of models. Moreover, we discuss hereditary properties for theta-lex and eta-weak dependence and illustrate the possible applications of the weak dependence notions to the study of the asymptotic properties of stationary random fields. Our general resu...
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作者：Fu, Yingjia; Williams, Ruth J.
作者单位：University of California System; University of California San Diego
摘要：This work concerns the asymptotic behavior of solutions to a critical fluid model for a data communication network, where file sizes are generally distributed and the network operates under a fair bandwidth sharing policy, chosen from the family of (weighted) alpha-fair policies introduced by Mo and Walrand (IEEE/ACM Trans. Netw. 8 (2000) 556-567). Solutions of the fluid model are measure-valued functions of time. Under law of large numbers scaling, Gromoll and Williams (Ann. Appl. Probab. 19 ...
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作者：Chassagneux, Jean-Francois; Szpruch, Lukasz; Tse, Alvin
作者单位：Universite Paris Cite; University of Edinburgh
摘要：Consider the metric space (P-2(R-d), W-2) of square integrable laws on R-d with the topology induced by the 2-Wasserstein distance W-2. Let Phi : P-2(R-d) -> R and mu is an element of P-2(R-d). In this work, we consider (a) mu(N) being the empirical measure of N-samples from mu, and the other case in which (b) mu(N) is the empirical measure of marginal laws of the particle system of a McKean-Vlasov PDE (mu(t))(t). The main result of this paper is to show that under suitable regularity conditio...
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作者：Adhikari, Kartick; Adler, Robert J.; Bobrowski, Omer; Rosenthal, Ron
作者单位：Technion Israel Institute of Technology; Technion Israel Institute of Technology
摘要：In this paper we study the spectrum of the random geometric graph G(n, r), in a regime where the graph is dense and highly connected. In the Erdos-Renyi G(n, p) random graph it is well known that upon connectivity the spectrum of the normalized graph Laplacian is concentrated around 1. We show that such concentration does not occur in the G(n, r) case, even when the graph is dense and almost a complete graph. In particular, we show that the limiting spectral gap is strictly smaller than 1. In ...
