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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：Goldberg, David A.
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：Recently, there has been significant interest in understanding the properties of Markov random fields (M.r.f.) defined on the independent sets of sparse graphs. When these M.r.f. are restricted to pairwise interactions (i.e., hardcore model), much progress has been made. However, considerably less is known in the presence of higher -order interactions, which arise, for example, in the analysis of independent sets with special properties and the study of resource-constrained communication netwo...
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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：Bibinger, Markus; Jirak, Moritz; Reiss, Markus
作者单位：University of Mannheim; Humboldt University of Berlin
摘要：For a semi-martingale X-t, which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation (X, X)(t) is constructed based on observations in the vicinity of X-t. The problem is embedded in a Poisson point process framework, which reveals an interesting connection to the theory of Brownian excursion areas. We derive n(-1/3) as optimal convergence rate in a high-frequency framework with n observations (in mean). We discuss a potential application for the estimation of the...
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作者：Cappelletti, Daniele; Wiuf, Carsten
作者单位：University of Copenhagen
摘要：We study networks of biochemical reactions modelled by continuous time Markov processes. Such networks typically contain many molecular species and reactions and are hard to study analytically as well as by simulation. Particularly, we are interested in reaction networks with intermediate species such as the substrate-enzyme complex in the Michaelis Menten mechanism. Such species are virtually in all real-world networks, they are typically short-lived, degraded at a fast rate and hard to obser...
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作者：Embrechts, Paul; Hofert, Marius; Wang, Ruodu
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Swiss Finance Institute (SFI); Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Waterloo
摘要：The tail-dependence compatibility problem is introduced. It raises the question whether a given d x d-matrix of entries in the unit interval is the matrix of pairwise tail-dependence coefficients of a d-dimensional random vector. The problem is studied together with Bernoulli-compatible matrices, that is, matrices which are expectations of outer products of random vectors with Bernoulli margins. We show that a square matrix with diagonal entries being 1 is a tail-dependence matrix if and only ...
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作者：Feng, Han; Hobson, David
作者单位：University of Warwick
摘要：This paper studies a variant of the contest model introduced in Seel and Strack [J. Econom. Theory 148 (2013) 2033-2048]. In the Seel-Strack contest, each agent or contestant privately observes a Brownian motion, absorbed at zero, and chooses when to stop it. The winner of the contest is the agent who stops at the highest value. The model assumes that all the processes start from a common value x(0) > 0 and the symmetric Nash equilibrium is for each agent to utilise a stopping rule which yield...
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作者：Yin, Mei; Rinaldo, Alessandro; Fadnavis, Sukhada
作者单位：University of Denver; Carnegie Mellon University; Harvard University
摘要：We describe the asymptotic properties of the edge-triangle exponential random graph model as the natural parameters diverge along straight lines. We show that as we continuously vary the slopes of these lines, a typical graph drawn from this model exhibits quantized behavior, jumping from one complete multipartite graph to another, and the jumps happen precisely at the normal lines of a polyhedral set with infinitely many facets. As a result, we provide a complete description of all asymptotic...
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作者：Jia, Chen; Jiang, Da-Quan; Qian, Min-Ping
作者单位：Chinese Academy of Engineering Physics; Beijing Computational Science Research Center (CSRC); Peking University; Peking University
摘要：In this paper, we find a series of equalities which characterize the symmetry of the forming times of a family of similar cycles for discrete-time and continuous-time Markov chains. Moreover, we use these cycle symmetries to study the circulation fluctuations for Markov chains. We prove that the sample circulations along a family of cycles passing through a common state satisfy a large deviation principle with a rate function which has a highly nonobvious symmetry. Further extensions and appli...
