6期

最新文章

• CENTRAL LIMIT THEOREMS OF A RECURSIVE STOCHASTIC ALGORITHM WITH APPLICATIONS TO ADAPTIVE DESIGNS AI翻译
  作者：Zhang, Li-Xin
  作者单位：Zhejiang University
  摘要：Stochastic approximation algorithms have been the subject of an enormous body of literature, both theoretical and applied. Recently, Laruelle and Pages [Ann. Appl. Probab. 23 (2013) 1409-1436] presented a link between the stochastic approximation and response-adaptive designs in clinical trials based on randomized urn models investigated in Bai and Hu [Stochastic Process. Appl. 80 (1999) 87-101; Ann. Appl. Probab. 15 (2005) 914-940], and derived the asymptotic normality or central limit theore...
• LATTICE APPROXIMATIONS OF REFLECTED STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS DRIVEN BY SPACE-TIME WHITE NOISE AI翻译
  作者：Zhang, Tusheng
  作者单位：University of Manchester
  摘要：We introduce a discretization/approximation scheme for reflected stochastic partial differential equations driven by space time white noise through systems of reflecting stochastic differential equations. To establish the convergence of the scheme, we study the existence and uniqueness of solutions of Skorohod-type deterministic systems on time-dependent domains. We also need to establish the convergence of an approximation scheme for deterministic parabolic obstacle problems. Both are of inde...
• ASYMPTOTIC QUANTIZATION OF EXPONENTIAL RANDOM GRAPHS AI翻译
  作者：Yin, Mei; Rinaldo, Alessandro; Fadnavis, Sukhada
  作者单位：University of Denver; Carnegie Mellon University; Harvard University
  摘要：We describe the asymptotic properties of the edge-triangle exponential random graph model as the natural parameters diverge along straight lines. We show that as we continuously vary the slopes of these lines, a typical graph drawn from this model exhibits quantized behavior, jumping from one complete multipartite graph to another, and the jumps happen precisely at the normal lines of a polyhedral set with infinitely many facets. As a result, we provide a complete description of all asymptotic...
• TRAPPING GAMES ON RANDOM BOARDS AI翻译
  作者：Basu, Riddhipratim; Holroyd, Alexander E.; Martin, James B.; Wastlund, Johan
  作者单位：Stanford University; Microsoft; University of Oxford; Chalmers University of Technology
  摘要：We consider the following two-player game on a graph. A token is located at a vertex, and the players take turns to move it along an edge to a vertex that has not been visited before. A player who cannot move loses. We analyze outcomes with optimal play on percolation clusters of Euclidean lattices. On Z(2) with two different percolation parameters for odd and even sites, we prove that the game has no draws provided closed sites of one parity are sufficiently rare compared with those of the ot...
• TRACY-WIDOM DISTRIBUTION FOR THE LARGEST EIGENVALUE OF REAL SAMPLE COVARIANCE MATRICES WITH GENERAL POPULATION AI翻译
  作者：Lee, Ji Oon; Schnelli, Kevin
  作者单位：Korea Advanced Institute of Science & Technology (KAIST); Institute of Science & Technology - Austria
  摘要：We consider sample covariance matrices of the form Q = (Sigma X-1/2)((EX)-X-1/2)*, where the sample X is an M x N random matrix whose entries are real independent random variables with variance 1/N and where Sigma is an M x M positive-definite deterministic matrix. We analyze the asymptotic fluctuations of the largest resealed eigenvalue of Q when both M and N tend to infinity with N/M -> d is an element of (0, infinity). For a large class of populations Sigma in the sub-critical regime, we sh...
• TRANSITION FROM GAUSSIAN TO NON-GAUSSIAN FLUCTUATIONS FOR MEAN-FIELD DIFFUSIONS IN SPATIAL INTERACTION AI翻译
  作者：Lucon, Eric; Stannat, Wilhelm
  作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Technical University of Berlin
  摘要：We consider a system of N disordered mean-field interacting diffusions within spatial constraints: each particle theta(i) is attached to one site x(i) of a periodic lattice and the interaction between particles theta(i) and theta(j) decreases as vertical bar x(i) - x(j)vertical bar(-alpha) for alpha is an element of [0, 1). In a previous work [Ann. Appl. Probab. 24 (2014) 1946-1993], it was shown that the empirical measure of the particles converges in large population to the solution of a non...
• COLLISION TIMES IN MULTICOLOR URN MODELS AND SEQUENTIAL GRAPH COLORING WITH APPLICATIONS TO DISCRETE LOGARITHMS AI翻译
  作者：Bhattacharya, Bhaswar B.
  作者单位：Stanford University
  摘要：Consider an urn model where at each step one of q colors is sampled according to some probability distribution and a ball of that color is placed in an urn. The distribution of assigning balls to urns may depend on the color of the ball. Collisions occur when a ball is placed in an urn which already contains a ball of different color. Equivalently, this can be viewed as sequentially coloring a complete q-partite graph wherein a collision corresponds to the appearance of a monochromatic edge. U...
• A FUNCTIONAL CENTRAL LIMIT THEOREM FOR BRANCHING RANDOM WALKS, ALMOST SURE WEAK CONVERGENCE AND APPLICATIONS TO RANDOM TREES AI翻译
  作者：Gruebel, Rudolf; Kabluchko, Zakhar
  作者单位：Leibniz University Hannover; University of Munster
  摘要：Let W-infinity (beta) be the limit of the Biggins martingale W-n(beta) associated to a supercritical branching random walk with mean number of offspring m. We prove a functional central limit theorem stating that as n -> infinity the process D-n(u) := m(1/2n) (W-infinity(u/root n) - W-n(u/root n)) converges weakly, on a suitable space of analytic functions, to a Gaussian random analytic function with random variance. Using this result, we prove central limit theorems for the total path length ...
• ARBITRAGE, HEDGING AND UTILITY MAXIMIZATION USING SEMI-STATIC TRADING STRATEGIES WITH AMERICAN OPTIONS AI翻译
  作者：Bayraktar, Erhan; Zhou, Zhou
  作者单位：University of Michigan System; University of Michigan; University of Minnesota System; University of Minnesota Twin Cities
  摘要：We consider a financial market where stocks are available for dynamic trading, and European and American options are available for static trading (semi-static trading strategies). We assume that the American options are infinitely divisible, and can only be bought but not sold. In the first part of the paper, we work within the framework without model ambiguity. We first get the fundamental theorem of asset pricing (FLAP). Using the FTAP, we get the dualities for the hedging prices of European...
• GENEALOGIES IN EXPANDING POPULATIONS AI翻译
  作者：Durrett, Rick; Fan, Wai-Tong (Louis)
  作者单位：Duke University; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine
  摘要：The goal of this paper is to prove rigorous results for the behavior of genealogies in a one-dimensional long range biased voter model introduced by Hallatschek and Nelson [Thew: Pop. Biol. 73 (2008) 158-170]. The first step, which is easily accomplished using results of Mueller and Tribe [Probab. Theory Related Fields 102 (1995) 519-545], is to show that when space and time are resealed correctly, our biased voter model converges to a Wright-Fisher SPDE. A simple extension of a result of Durr...