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作者：Chen, Yue; Busic, Ana; Meyn, Sean
作者单位：State University System of Florida; University of Florida; Inria; Universite PSL; Ecole Normale Superieure (ENS)
摘要：Consider a stochastic process X on a finite state space X = {1,...,}d. It is conditionally Markov, given a real-valued input process sigma.0 This is assumed to be small, which is modeled through the scaling, sigma(t) = epsilon sigma(1)(t), 0 <= epsilon <= 1, where sigma(1) is a bounded stationary process. The following conclusions are obtained, subject to smoothness assumptions on the controlled transition matrix and a mixing condition on sigma : (i) A stationary version of the process is cons...
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作者：Briand, Philippe; Elie, Romuald; Hu, Ying
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Savoie Mont Blanc; CNRS - National Institute for Mathematical Sciences (INSMI); CNRS - Institute of Physics (INP); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite Gustave-Eiffel; Inria; Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：In this paper, we study a new type of BSDE, where the distribution of the Y-component of the solution is required to satisfy an additional constraint, written in terms of the expectation of a loss function. This constraint is imposed at any deterministic time t and is typically weaker than the classical pointwise one associated to reflected BSDEs. Focusing on solutions (Y, Z, K) with deterministic K, we obtain the well-posedness of such equation, in the presence of a natural Skorokhod-type con...
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作者：Bhamidi, Shankar; Jin, Jimmy; Nobel, Andrew
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：Inspired by empirical data on real world complex networks, the last few years have seen an explosion in proposed generative models to understand and explain observed properties of real world networks, including power law degree distribution and small world distance scaling. In this context, a natural question is how to understand the effect of change points-how abrupt changes in parameters driving the network model change structural properties of the network. We study this phenomenon in one po...
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作者：Fernholz, E. Robert; Karatzas, Ioannis; Ruf, Johannes
作者单位：Columbia University; University of London; London School Economics & Political Science
摘要：in an equity market consisting of a fixed number d of assets with capitalization weights mu(i) (.), is an observable and a nondecreasing function of time. If this observable of the market is not just nondecreasing but actually grows at a rate bounded away from zero, then strong arbitrage can be constructed relative to the market over sufficiently long time horizons. It has been an open issue for more than ten years, whether such strong outperformance of the market is possible also over arbitra...
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作者：Jacod, Jean; Todorov, Viktor
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite; Northwestern University
摘要：We derive limit theorems for functionals of local empirical characteristic functions constructed from high-frequency observations of Ito semimartingales contaminated with noise. In a first step, we average locally the data to mitigate the effect of the noise, and then in a second step, we form local empirical characteristic functions from the pre-averaged data. The final statistics are formed by summing the local empirical characteristic exponents over the observation interval. The limit behav...
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作者：Budhiraja, Amarjit; Friedlander, Eric
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We consider a rate control problem for an N-particle weakly interacting finite state Markov process. The process models the state evolution of a large collection of particles and allows for multiple particles to change state simultaneously. Such models have been proposed for large communication systems (e.g., ad hoc wireless networks) but are also suitable for other settings such as chemical-reaction networks. An associated diffusion control problem is presented and we show that the value func...
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作者：Fountoulakis, Nikolaos; Mueller, Tobias
作者单位：University of Birmingham; Utrecht University; University of Groningen
摘要：We consider the component structure of a recent model of random graphs on the hyperbolic plane that was introduced by Krioukov et al. The model exhibits a power law degree sequence, small distances and clustering, features that are associated with so-called complex networks. The model is controlled by two parameters alpha and nu where, roughly speaking, alpha controls the exponent of the power law and nu controls the average degree. Refining earlier results, we are able to show a law of large ...
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作者：Alt, Johannes; Erdos, Laszlo; Krueger, Torben
作者单位：Institute of Science & Technology - Austria
摘要：We consider large random matrices X with centered, independent entries, which have comparable but not necessarily identical variances. Girko's circular law asserts that the spectrum is supported in a disk and in case of identical variances, the limiting density is uniform. In this special case, the local circular law by Bourgade et al. [Probab. Theory Related Fields 159 (2014) 545-595; Probab. Theory Related Fields 159 (2014) 619-660] shows that the empirical density converges even locally on ...
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作者：De Angelis, Tiziano; Ferrari, Giorgio; Moriarty, John
作者单位：University of Leeds; University of Bielefeld; University of London; Queen Mary University London
摘要：This paper analyses two-player nonzero-sum games of optimal stopping on a class of linear regular diffusions with not nonsingular boundary behaviour [in the sense of Ito and McKean (Diffusion Processes and Their Sample Paths (1974) Springer, page 108)]. We provide sufficient conditions under which Nash equilibria are realised by each player stopping the diffusion at one of the two boundary points of an interval. The boundaries of this interval solve a system of algebraic equations. We also pro...
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作者：Biskup, Marek; Procaccia, Eviatar B.
作者单位：University of California System; University of California Los Angeles; Charles University Prague; Texas A&M University System; Texas A&M University College Station
摘要：We study paths of time-length t of a continuous-time random walk on Z(2) subject to self-interaction that depends on the geometry of the walk range and a collection of random, uniformly positive and finite edge weights. The interaction enters through a Gibbs weight at inverse temperature beta; the energy is the total sum of the edge weights for edges on the outer boundary of the range. For edge weights sampled from a translation-invariant, ergodic law, we prove that the range boundary condensa...
