-
作者：Bierkens, Joris; Roberts, Gareth
作者单位：Delft University of Technology; University of Warwick
摘要：In Turitsyn, Chertkov and Vucelja [Phys. D 240 (2011) 410-414] a nonreversible Markov Chain Monte Carlo (MCMC) method on an augmented state space was introduced, here referred to as Lifted Metropolis Hastings (LMH). A scaling limit of the magnetization process in the Curie Weiss model is derived for LMH, as well as for Metropolis Hastings (MH). The required jump rate in the high (supercritical) temperature regime equals n(1/2) for LMH, which should be compared to n for MH. At the critical temp...
-
作者：Kaellblad, Sigrid; Tan, Xiaolu; Touzi, Nizar
作者单位：Technische Universitat Wien; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique
摘要：We consider the optimal Skorokhod embedding problem (SEP) given full marginals over the time interval [0,1]. The problem is related to the study of extremal martingales associated with a peacock (process increasing in convex order, by Hirsch, Profeta, Roynette and Yor [Peacocks and Associated Martingales, with Explicit Constructions (2011), Springer, Milan]). A general duality result is obtained by convergence techniques. We then study the case where the reward function depends on the maximum ...
-
作者：Johnson, Peter; Peskir, Goran
作者单位：University of Manchester
摘要：Consider the motion of a Brownian particle that initially takes place in a two-dimensional plane and then after some random/unobservable time continues in the three-dimensional space. Given that only the distance of the particle to the origin is being observed, the problem is to detect the time at which the particle departs from the plane as accurately as possible. We solve this problem in the most uncertain scenario when the random/unobservable time is (i) exponentially distributed and (ii) i...
-
作者：Kolodziejek, Bartosz
作者单位：Warsaw University of Technology
摘要：In this paper, we show under weak assumptions that for R = (d) 1 + M-1 M1M2 + . . ., where P(M is an element of [0, 1]) = 1 and M-i are independent copies of M, we have lnP(R > x) similar to CxlnP(M > 1 - 1/x) as x -> infinity. The constant C is given explicitly and its value depends on the rate of convergence of 1nP(M > 1 - 1/x). Random variable R satisfies the stochastic equation R 1 + MR with M and R independent, thus this result fits into the study of tails of iterated random equations, or...
-
作者：Bierme, Hermine; Durieu, Olivier; Wang, Yizao
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Poitiers; Centre National de la Recherche Scientifique (CNRS); University System of Ohio; University of Cincinnati
摘要：Recently, Hammond and Sheffield [Probab. Theory Related Fields 157 (2013) 691-719] introduced a model of correlated one-dimensional random walks that scale to fractional Brownian motions with long-range dependence. In this paper, we consider a natural generalization of this model to dimension d >= 2. We define a Z(d)-indexed random field with dependence relations governed by an underlying random graph with vertices Z(d), and we study the scaling limits of the partial sums of the random field o...
-
作者：Fischer, Markus
作者单位：University of Padua
摘要：Mean field games are limit models for symmetric N-player games with interaction of mean field type as N -> infinity. The limit relation is often understood in the sense that a solution of a mean field game allows to construct approximate Nash equilibria for the corresponding N-player games. The opposite direction is of interest, too: When do sequences of Nash equilibria converge to solutions of an associated mean field game? In this direction, rigorous results are mostly available for stationa...
-
作者：Laruelle, Sophie; Pages, Gilles
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite
-
作者：Ball, Frank; Neal, Peter
作者单位：University of Nottingham; Lancaster University
摘要：For a supercritical configuration model random graph, it is well known that, subject to mild conditions, there exists a unique giant component, whose size R-n is O (n), where n is the total number of vertices in the random graph. Moreover, there exists 0 < rho <= 1 such that R-n/n ->(p) rho as n -> infinity. We show that for a sequence of well behaved configuration model random graphs with a deterministic degree sequence satisfying 0 < rho < 1; there exists sigma(2) > 0, such that var(root n(R...
-
作者：Mourrat, Jean-Christophe; Nolen, James
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON); Duke University
摘要：In the homogenization of divergence-form equations with random coefficients, a central role is played by the corrector. We focus on a discrete space setting and on dimension 3 and more. Under a minor smoothness assumption on the law of the random coefficients, we identify the scaling limit of the corrector, which is akin to a Gaussian free field. This completes the argument started in [Ann. Probab. 44 (2016) 3207-3233].
-
作者：Gaunt, Robert E.; Pickett, Alastair M.; Reinert, Gesine
作者单位：University of Oxford
摘要：This paper concerns the development of Stein's method for chi-square approximation and its application to problems in statistics. New bounds for the derivatives of the solution of the gamma Stein equation are obtained. These bounds involve both the shape parameter and the order of the derivative. Subsequently, Stein's method for chi-square approximation is applied to bound the distributional distance between Pearson's statistic and its limiting chi-square distribution, measured using smooth te...
