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作者：Glatt-holtz, Nathan; Krometis, Justin; Mondaini, Cecilia
作者单位：Tulane University; Virginia Polytechnic Institute & State University; Virginia Polytechnic Institute & State University; Drexel University
摘要：This work develops a powerful and versatile framework for determin-ing acceptance ratios in Metropolis-Hastings-type Markov kernels widely used in statistical sampling problems. Our approach allows us to derive new classes of kernels which unify random walk or diffusion-type sampling meth-ods with more complicated extended phase space algorithms based around ideas from Hamiltonian dynamics. Our starting point is an abstract result de-veloped in the generality of measurable state spaces that ad...
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作者：Cai, Xing shi; Caputo, Pietro; Perarnau, Guillem; Quattropani, Matteo
作者单位：Duke Kunshan University; Roma Tre University; Centre de Recerca Matematica (CRM); Universitat Politecnica de Catalunya; Sapienza University Rome
摘要：We consider the extremal values of the stationary distribution of sparse directed random graphs with given degree sequences and their relation to the extremal values of the in-degree sequence. The graphs are generated by the directed configuration model. Under the assumption of bounded (2 + eta)moments on the in-degrees and of bounded out-degrees, we obtain tight comparisons between the maximum value of the stationary distribution and the maximum in-degree. Under the further assumption that th...
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作者：Gurvich, Itai
作者单位：Northwestern University
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作者：Fukasawa, Masaaki; Ugai, Takuto
作者单位：University of Osaka
摘要：Our study aims to specify the asymptotic error distribution in the dis-cretization of a stochastic Volterra equation with a fractional kernel. It is well known that for a standard stochastic differential equation, the discretization error, normalized with its rate of convergence 1/root n, converges in law to the solution of a certain linear equation. Similar to this, we show that a suitably normalized discretization error of the Volterra equation converges in law to the solution of a certain l...
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作者：Mueller, Carl; Neuman, Eyal
作者单位：University of Rochester; Imperial College London
摘要：We study elastic manifolds with self-repelling terms and estimate their effective radius. This class of manifolds is modelled by a self-repelling vector-valued Gaussian free field with Neumann boundary conditions over the domain [-N,N](d)boolean AND Z(d), that takes values in R-d. Our main result states that in two dimensions (d=2), the effective radius R-N of the manifold is approximately N. This verifies the conjecture of Kantor, Kardar and Nelson (Phys. Rev. Lett. 58 (1987) 1289-1292) up to...
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作者：Carmona, Rene; Lauriere, Mathieu; Tan, Zongjun
作者单位：Princeton University; New York University; NYU Shanghai; New York University; NYU Shanghai
摘要：We study infinite horizon discounted mean field control (MFC) prob-lems with common noise through the lens of mean field Markov decision processes (MFMDP). We allow the agents to use actions that are randomized not only at the individual level but also at the level of the population. This common randomization is introduced for the purpose of exploration from a reinforcement learning (RL) paradigm. It also allows us to establish connec-tions between both closed-loop and open-loop policies for M...
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作者：Zhou, Jianjun
作者单位：Northwest A&F University - China
摘要：In this article a notion of viscosity solutions is introduced for second -order path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with optimal control problems for path-dependent stochastic differential equations. We identify the value functional of optimal control problems as unique viscosity solution to the associated PHJB equations. We also show that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions and satisfies a stabilit...
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作者：Beiglboeck, Mathias; Jourdain, Benjamin; Margheriti, William; Pammer, Gudmund
作者单位：University of Vienna; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：While many questions in (robust) finance can be posed in the martingale optimal transport (MOT) framework, others require to consider also nonlinear cost functionals. Following the terminology of Gozlan, Roberto, Samson and Tetali (J. Funct. Anal. 273 (2017) 3327-3405) for classical optimal transport, this corresponds to weak martingale optimal transport (WMOT).In this article we establish stability of WMOT which is important since financial data can give only imprecise information on the unde...
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作者：Doukhan, Paul; Neumann, Michael h.; Truquet, Lionel
作者单位：CY Cergy Paris Universite; Friedrich Schiller University of Jena
摘要：The first motivation of this paper is to study stationarity and ergodic properties for a general class of time series models defined conditional on an exogenous covariates process. The dynamic of these models is given by an autoregressive latent process which forms a Markov chain in random environments. Contrarily to existing contributions in the field of Markov chains in random environments, the state space is not discrete and we do not use small set type assumptions or uniform contraction co...
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作者：Feng, Renjie; Tian, Gang; Wei, Dongyi
作者单位：Max Planck Society; Peking University
摘要：We will prove the Berry-Esseen theorem for the number counting function of the circular beta-ensemble (C beta E), which will imply the central limit theorem for the number of points in arcs of the unit circle in mesoscopic and macroscopic scales. We will prove the main result by estimating the characteristic functions of the Prufer phases and the number counting function, which will imply the uniform upper and lower bounds of their variance. We also show that the similar results hold for the S...
