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作者：Barrera, Gerardo; Jara, Milton
作者单位：University of Alberta; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We consider an ordinary differential equation with a unique hyperbolic attractor at the origin, to which we add a small random perturbation. It is known that under general conditions, the solution of this stochastic differential equation converges exponentially fast to an equilibrium distribution. We show that the convergence occurs abruptly: in a time window of small size compared to the natural time scale of the process, the distance to equilibrium drops from its maximal possible value to ne...
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作者：Bou-Rabee, Nawaf; Eberle, Andreas; Zimmer, Raphael
作者单位：Rutgers University System; Rutgers University Camden; University of Bonn
摘要：Based on a new coupling approach, we prove that the transition step of the Hamiltonian Monte Carlo algorithm is contractive w.r.t. a carefully designed Kantorovich (L-1 Wasserstein) distance. The lower bound for the contraction rate is explicit. Global convexity of the potential is not required, and thus multimodal target distributions are included. Explicit quantitative bounds for the number of steps required to approximate the stationary distribution up to a given error epsilon are a direct ...
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作者：Wang, Neng-Yi; Wu, Liming
作者单位：Huazhong University of Science & Technology; Universite Clermont Auvergne (UCA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：This paper is the discrete time counterpart of the previous work in the continuous time case by Guillin, Leonard, the second named author and Yao [Probab. Theory Related Fields 144 (2009), 669-695]. We investigate the following transport-information TvI inequality: alpha(T-v(nu, mu)) <= I(nu vertical bar P, mu) for all probability measures nu on some metric space (X, d), where mu is an invariant and ergodic probability measure of some given transition kernel P (x, dy), T-v(nu, mu) is some tran...
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作者：Ernst, P. A.; Peskir, G.; Zhou, Q.
作者单位：Rice University; University of Manchester; Texas A&M University System; Texas A&M University College Station
摘要：Consider the motion of a Brownian particle in three dimensions, whose two spatial coordinates are standard Brownian motions with zero drift, and the remaining (unknown) spatial coordinate is a standard Brownian motion with a (known) nonzero drift. Given that the position of the Brownian particle is being observed in real time, the problem is to detect as soon as possible and with minimal probabilities of the wrong terminal decisions, which spatial coordinate has the nonzero drift. We solve thi...
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作者：Ascione, Giacomo; Pirozzi, Enrica; Toaldo, Bruno
作者单位：University of Naples Federico II; University of Turin
摘要：In this paper we characterize the distribution of the first exit time from an arbitrary open set for a class of semi-Markov processes obtained as time-changed Markov processes. We estimate the asymptotic behaviour of the survival function (for large t) and of the distribution function (for small t) and we provide some conditions for absolute continuity. We have been inspired by a problem of neurophyshiology and our results are particularly usefull in this field, precisely for the so-called Lea...
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作者：Possamai, Dylan; Touzi, Nizar; Zhang, Jianfeng
作者单位：Columbia University; Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique; University of Southern California
摘要：We consider zero-sum stochastic differential games with possibly path-dependent volatility controls. Unlike the previous literature, we allow for weak solutions of the state equation so that the players' controls are automatically of feedback type. In particular, we do not require the controls to be simple, which has fundamental importance for the possible existence of saddle-points. Under some restrictions, needed for the a priori regularity of the upper and lower value functions of the game,...
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作者：Backhoff-Veraguas, Julio; Lacker, Daniel; Tangpi, Ludovic
作者单位：University of Vienna; Columbia University; Princeton University
摘要：We derive new limit theorems for Brownian motion, which can be seen as nonexponential analogues of the large deviation theorems of Sanov and Schilder in their Laplace principle forms. As a first application, we obtain novel scaling limits of backward stochastic differential equations and their related partial differential equations. As a second application, we extend prior results on the small-noise limit of the Schrodinger problem as an optimal transport cost, unifying the control-theoretic a...
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作者：Mueller, Tobias; Penrose, Mathew D.
作者单位：University of Groningen; University of Bath
摘要：Let d >= 2. The Cheeger constant of a graph is the minimum surface-to-volume ratio of all subsets of the vertex set with relative volume at most 1/2. There are several ways to define surface and volume here: the simplest method is to count boundary edges (for the surface) and vertices (for the volume). We show that for a geometric (possibly weighted) graph on n random points in a d-dimensional domain with Lipschitz boundary and with distance parameter decaying more slowly (as a function of n) ...
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作者：Abbe, Emmanuel; Boix-Adsera, Enric
作者单位：Princeton University; Princeton University
摘要：This paper considers the problem of reconstructing n independent uni- form spins X-1,...,X-n living on the vertices of an n-vertex graph G, by observing their interactions on the edges of the graph. This captures instances of models such as (i) broadcasting on trees, (ii) block models, (iii) synchronization on grids, (iv) spiked Wigner models. The paper gives an upper bound on the mutual information between two vertices in terms of a bond percolation estimate. Namely, the information between t...
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作者：Betz, Volker; Schaefer, Helge; Zeindler, Dirk
作者单位：Technical University of Darmstadt; Lancaster University
摘要：We consider uniform random permutations of length n conditioned to have no cycle longer than n(beta) with 0 < beta < 1, in the limit of large n. Since in unconstrained uniform random permutations most of the indices are in cycles of macroscopic length, this is a singular conditioning in the limit. Nevertheless, we obtain a fairly complete picture about the cycle number distribution at various lengths. Depending on the scale at which cycle numbers are studied, our results include Poisson conver...
