The Annals of Applied Probability

最新文章

• STRONG LIMIT OF THE EXTREME EIGENVALUES OF A SYMMETRIZED AUTO-CROSS COVARIANCE MATRIX AI翻译
  作者：Wang, Chen; Jin, Baisuo; Bai, Z. D.; Nair, K. Krishnan; Harding, Matthew
  作者单位：National University of Singapore; Chinese Academy of Sciences; University of Science & Technology of China, CAS; Northeast Normal University - China; Northeast Normal University - China; Stanford University; Duke University
  摘要：The auto-cross covariance matrix is defined as M-n = 1/2T Sigma(T)(j=1) (e(j)e(j+pi)* + e(j+tau)e(j)*), where e(j)'s are n-dimensional vectors of independent standard complex components with a common mean 0, variance sigma(2), and uniformly bounded 2 + eta th moments and tau is the lag. Jin et al. [Ann. AppL Probab. 24 (2014) 119912251 has proved that the LSD of M-n exists uniquely and nonrandomly, and independent of tau for all tau >= 1. And in addition they gave an analytic expression of the...
• CAN LOCAL PARTICLE FILTERS BEAT THE CURSE OF DIMENSIONALITY? AI翻译
  作者：Rebeschini, Patrick; van Handel, Ramon
  作者单位：Princeton University
  摘要：The discovery of particle filtering methods has enabled the use of nonlinear filtering in a wide array of applications. Unfortunately, the approximation error of particle filters typically grows exponentially in the dimension of the underlying model. This phenomenon has rendered particle filters of limited use in complex data assimilation problems. In this paper, we argue that it is often possible, at least in principle, to develop local particle filtering algorithms whose approximation error ...
• DEGREE DISTRIBUTION OF SHORTEST PATH TREES AND BIAS OF NETWORK SAMPLING ALGORITHMS AI翻译
  作者：Bhamidi, Shankar; Goodman, Jesse; van der Hofstad, Remco; Komjathy, Julia
  作者单位：University of North Carolina; University of North Carolina Chapel Hill; Technion Israel Institute of Technology; Eindhoven University of Technology
  摘要：In this article, we explicitly derive the limiting degree distribution of the shortest path tree from a single source on various random network models with edge weights. We determine the asymptotics of the degree distribution for large degrees of this tree and compare it to the degree distribution of the original graph. We perform this analysis for the complete graph with edge weights that are powers of exponential random variables (weak disorder in the stochastic mean-field model of distance)...
• APPROXIMATION ALGORITHMS FOR THE NORMALIZING CONSTANT OF GIBBS DISTRIBUTIONS AI翻译
  作者：Huber, Mark
  作者单位：Claremont Colleges; Claremont McKenna College; Claremont Graduate University
  摘要：Consider a family of distributions {pi(beta)} where X similar to pi(beta) means that P(X = x) = exp(-beta H(x))/Z(beta). Here Z(beta) is the proper normalizing constant, equal to Sigma(x) exp(-beta H(x)). Then {pi(beta)} is known as a Gibbs distribution, and Z(beta) is the partition function. This work presents a new method for approximating the partition function to a specified level of relative accuracy using only a number of samples, that is, O(ln(Z(beta) ln(ln(Z(beta)))) when Z(0) >= 1. Th...
• OPTIMAL STOPPING UNDER ADVERSE NONLINEAR EXPECTATION AND RELATED GAMES AI翻译
  作者：Nutz, Marcel; Zhang, Jianfeng
  作者单位：Columbia University; University of Southern California
  摘要：We study the existence of optimal actions in a zero-sum game inf(tau) sup(P) E-P [X-tau] between a stopper and a controller choosing a probability measure. This includes the optimal stopping problem inf(tau) epsilon(X-tau) for a class of sublinear expectations epsilon(.) such as the G-expectation. We show that the game has a value. Moreover, exploiting the theory of sublinear expectations, we define a nonlinear Snell envelope Y and prove that the first hitting time inf{t : Y-t = X-t} is an opt...
• SPACE-TIME PERCOLATION AND DETECTION BY MOBILE NODES AI翻译
  作者：Stauffer, Alexandre
  作者单位：University of Bath
  摘要：Consider the model where nodes are initially distributed as a Poisson point process with intensity lambda over R-d and are moving in continuous time according to independent Brownian motions. We assume that nodes are capable of detecting all points within distance r of their location and study the problem of determining the first time at which a target particle, which is initially placed at the origin of R-d, is detected by at least one node. We consider the case where the target particle can ...
• ON WELL-POSEDNESS OF FORWARD-BACKWARD SDES-A UNIFIED APPROACH AI翻译
  作者：Ma, Jin; Wu, Zhen; Zhang, Detao; Zhang, Jianfeng
  作者单位：University of Southern California; Shandong University
  摘要：In this paper, we study the well-posedness of the Forward Backward Stochastic Differential Equations (FBSDE) in a general non-Markovian framework. The main purpose is to find a unified scheme which combines all existing methodology in the literature, and to address some fundamental long-standing problems for non-Markovian FBSDEs. An important device is a decoupling random field that is regular (uniformly Lipschitz in its spatial variable). We show that the regulariy of such decoupling field is...
• GIBBS MEASURES ON PERMUTATIONS OVER ONE-DIMENSIONAL DISCRETE POINT SETS AI翻译
  作者：Biskup, Marek; Richthammer, Thomas
  作者单位：University of California System; University of California Los Angeles; University of South Bohemia Ceske Budejovice; University of Hildesheim; University of Hildesheim
  摘要：We consider Gibbs distributions on permutations of a locally finite infinite set X subset of R, where a permutation sigma of X is assigned (formal) energy Sigma(x is an element of X) V(sigma(x) - x). This is motivated by Feynman's path representation of the quantum Bose gas; the choice X := Z and V(x) := alpha x(2) is of principal interest. Under suitable regularity conditions on the set X and the potential V, we establish existence and a full classification of the infinite-volume Gibbs measur...
• CENTRAL LIMIT THEOREM FOR THE MULTILEVEL MONTE CARLO EULER METHOD AI翻译
  作者：Ben Alaya, Mohamed; Kebaier, Armed
  作者单位：Universite Paris 13; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
  摘要：This paper focuses on studying the multilevel Monte Carlo method recently introduced by Giles [Oper. Res. 56 (2008) 607-617] which is significantly more efficient than the classical Monte Carlo one. Our aim is to prove a central limit theorem of Lindeberg Feller type for the multilevel Monte Carlo method associated with the Euler discretization scheme. To do so, we prove first a stable law convergence theorem, in the spirit of Jacod and Protter [Ann. Probab. 26 (1998) 267-307], for the Euler s...
• A GEOMETRIC ACHLIOPTAS PROCESS AI翻译
  作者：Muller, Tobias; Spoehel, Reto
  作者单位：Utrecht University
  摘要：The random geometric graph is obtained by sampling n points from the unit square (uniformly at random and independently), and connecting two points whenever their distance is at most r, for some given r = r(n). We consider the following variation on the random geometric graph: in each of n rounds in total, a player is offered two random points from the unit square, and has to select exactly one of these two points for inclusion in the evolving geometric graph. We study the problem of avoiding ...