The Annals of Applied Probability

最新文章

• A THRESHOLD FOR CUTOFF IN TWO-COMMUNITY RANDOM GRAPHS AI翻译
  作者：Ben-Hamou, Anna
  作者单位：Universite Paris Cite; Sorbonne Universite
  摘要：In this paper, we are interested in the impact of communities on the mixing behavior of the nonbacktracking random walk. We consider sequences of sparse random graphs of size N generated according to a variant of the classical configuration model which incorporates a two-community structure. The strength of the bottleneck is measured by a parameter alpha which roughly corresponds to the fraction of edges that go from one community to the other. We show that if alpha >> 1/ log N, then the nonba...
• GLOBAL C1 REGULARITY OF THE VALUE FUNCTION IN OPTIMAL STOPPING PROBLEMS AI翻译
  作者：De Angelis, T.; Peskir, G.
  作者单位：University of Leeds; University of Manchester
  摘要：We show that if either the process is strong Feller and the boundary point is probabilistically regular for the stopping set, or the process is strong Markov and the boundary point is probabilistically regular for the interior of the stopping set, then the boundary point is Green regular for the stopping set. Combining this implication with the existence of a continuously differentiable flow of the process we show that the value function is continuously differentiable at the optimal stopping b...
• STATISTICAL THRESHOLDS FOR TENSOR PCA AI翻译
  作者：Jagannath, Aukosh; Lopatto, Patrick; Miolane, Leo
  作者单位：Harvard University; University of Waterloo; University of Waterloo; Inria; Universite PSL; Ecole Normale Superieure (ENS)
  摘要：We study the statistical limits of testing and estimation for a rank one deformation of a Gaussian random tensor. We compute the sharp thresholds for hypothesis testing and estimation by maximum likelihood and show that they are the same. Furthermore, we find that the maximum likelihood estimator achieves the maximal correlation with the planted vector among measurable estimators above the estimation threshold. In this setting, the maximum likelihood estimator exhibits a discontinuous BBP-type...
• THE INVERSE FIRST PASSAGE TIME PROBLEM FOR KILLED BROWNIAN MOTION AI翻译
  作者：Ettinger, Boris; Hening, Alexandru; Wong, Tak Kwong
  作者单位：Tufts University; University of Hong Kong
  摘要：The classical inverse first passage time problem asks whether, for a Brownian motion (B-t)(t >= 0) and a positive random variable xi, there exists a barrier b : R+ -> R such that P{B-s > b(s), 0 <= s <= t} = P{xi> t}, for all t >= 0. We study a variant of the inverse first passage time problem for killed Brownian motion. We show that if lambda > 0 is a killing rate parameter and 1((-infinity,)(0]) is the indicator of the set (-infinity, 0] then, under certain compatibility assumptions, there e...
• ON THE ASYMPTOTIC OPTIMALITY OF THE COMB STRATEGY FOR PREDICTION WITH EXPERT ADVICE AI翻译
  作者：Bayraktar, Erhan; Ekren, Ibrahim; Zhang, Yili
  作者单位：University of Michigan System; University of Michigan; State University System of Florida; Florida State University
  摘要：For the problem of prediction with expert advice in the adversarial setting with geometric stopping, we compute the exact leading order expansion for the long time behavior of the value function. Then, we use this expansion to prove that as conjectured in Gravin, Peres and Sivan (In Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms (2016) 528-547, ACM), the comb strategies are indeed asymptotically optimal for the adversary in the case of 4 experts.
• SAMPLE PATH LARGE DEVIATIONS FOR LEVY PROCESSES AND RANDOM WALKS WITH WEIBULL INCREMENTS AI翻译
  作者：Bazhba, Mihail; Blanchet, Jose; Rhee, Chang-Han; Zwart, Bert
  作者单位：Stanford University; Northwestern University
  摘要：We study sample path large deviations for Levy processes and random walks with heavy-tailed jump-size distributions that are of Weibull type. The sharpness and applicability of these results are illustrated by a counterexample proving the nonexistence of a full LDP in the J(1) topology, and by an application to a first passage problem.
• SPATIAL GROWTH PROCESSES WITH LONG RANGE DISPERSION: MICROSCOPICS, MESOSCOPICS AND DISCREPANCY IN SPREAD RATE AI翻译
  作者：Bezborodov, Viktor; Di Persio, Luca; Krueger, Tyll; Tkachov, Pasha
  作者单位：Wroclaw University of Science & Technology; University of Verona; Gran Sasso Science Institute (GSSI)
  摘要：We consider the speed of propagation of a continuous-time continuous-space branching random walk with the additional restriction that the birth rate at any spatial point cannot exceed 1. The dispersion kernel is taken to have density that decays polynomially as vertical bar x vertical bar(-2 alpha) , x -> infinity. We show that if alpha > 2, then the system spreads at a linear speed, while for alpha is an element of (1/2, 2] the spread is faster than linear. We also consider the mesoscopic equ...
• IMAGINARY MULTIPLICATIVE CHAOS: MOMENTS, REGULARITY AND CONNECTIONS TO THE ISING MODEL AI翻译
  作者：Junnila, Janne; Saksman, Eero; Webb, Christian
  作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Norwegian University of Science & Technology (NTNU); Aalto University
  摘要：In this article we study imaginary Gaussian multiplicative chaos-namely a family of random generalized functions which can formally be written as e(iX(x)), where X is a log-correlated real-valued Gaussian field on R-d, that is, it has a logarithmic singularity on the diagonal of its covariance. We study basic analytic properties of these random generalized functions, such as what spaces of distributions these objects live in, along with their basic stochastic properties, such as moment and tai...
• PARTICLES SYSTEMS AND NUMERICAL SCHEMES FOR MEAN REFLECTED STOCHASTIC DIFFERENTIAL EQUATIONS AI翻译
  作者：Briand, Philippe; De Raynal, Paul-Eric Chaudru; Guillin, Arnaud; Labart, Celine
  作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Savoie Mont Blanc; Universite Clermont Auvergne (UCA); Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS)
  摘要：This paper is devoted to the study of reflected Stochastic Differential Equations when the constraint is not on the paths of the solution but acts on its law. These reflected equations have been introduced recently in a backward form by Briand, Elie and Hu (Ann. Appl. Probab. 28 (2018) 482-510) in the context of risk measures. We here focus on the forward version of such reflected equations. Our main objective is to provide an approximation of the solutions with the help of interacting particl...
• VISCOSITY SOLUTIONS TO PARABOLIC MASTER EQUATIONS AND MCKEAN-VLASOV SDES WITH CLOSED-LOOP CONTROLS AI翻译
  作者：Wu, Cong; Zhang, Jianfeng
  作者单位：University of Southern California
  摘要：The master equation is a type of PDE whose state variable involves the distribution of certain underlying state process. It is a powerful tool for studying the limit behavior of large interacting systems, including mean field games and systemic risk. It also appears naturally in stochastic control problems with partial information and in time inconsistent problems. In this paper we propose a novel notion of viscosity solution for parabolic master equations, arising mainly from control problems...