The Annals of Applied Probability

最新文章

• A DISCRETE COMPLEMENT OF LYAPUNOV'S INEQUALITY AND ITS INFORMATION THEORETIC CONSEQUENCES AI翻译
  作者：Elbourne, James m; Palafox -castillo, Gerardo
  作者单位：Universidad Autonoma de Nuevo Leon
  摘要：We establish a reversal of Lyapunov's inequality for monotone logconcave sequences, settling a conjecture of Havrilla-Tkocz and Melbourne- Tkocz. A strengthened version of the same conjecture is disproved through counter example. We also derive several information theoretic inequalities as consequences. In particular sharp bounds are derived for the varentropy, Renyi entropies, and the concentration of information of monotone logconcave random variables. Moreover, the majorization approach uti...
• PROBABILISTIC AND ANALYTICAL PROPERTIES OF THE LAST PASSAGE PERCOLATION CONSTANT IN A WEIGHTED RANDOM DIRECTED GRAPH AI翻译
  作者：Foss, Sergey; Konstantopoulos, Takis; Pyatkin, Artem
  作者单位：Heriot Watt University; University of Liverpool; Russian Academy of Sciences; Sobolev Institute of Mathematics
  摘要：To each edge (i, j), i < j, of the complete directed graph on the integers we assign unit weight with probability p or weight x with probability 1 - p, independently from edge to edge, and give to each path weight equal to the sum of its edge weights. If Wx0,n is the maximum weight of all paths from 0 to n then Wx0,n/n -> Cp(x), as n -> infinity, almost surely, where Cp(x)is positive and deterministic. We study Cp(x) as a function of x, for fixed 0 < p < 1, and show that it is a strictly incre...
• APPROXIMATION BOUNDS FOR RANDOM NEURAL NETWORKS AND RESERVOIR SYSTEMS AI翻译
  作者：Gonon, Lukas; Grigoryeva, Lyudmila; Ortega, Juan-pablo
  作者单位：University of Munich; University of Warwick; Nanyang Technological University
  摘要：This work studies approximation based on single-hidden-layer feed -forward and recurrent neural networks with randomly generated internal weights. These methods, in which only the last layer of weights and a few hy-perparameters are optimized, have been successfully applied in a wide range of static and dynamic learning problems. Despite the popularity of this ap-proach in empirical tasks, important theoretical questions regarding the rela-tion between the unknown function, the weight distribu...
• SAMPLING FROM POTTS ON RANDOM GRAPHS OF UNBOUNDED DEGREE VIA RANDOM-CLUSTER DYNAMICS AI翻译
  作者：Blanca, Antonio; Gheissari, Reza
  作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of California System; University of California Berkeley; University of California System; University of California Berkeley
  摘要：We consider the problem of sampling from the ferromagnetic Potts and random-cluster models on a general family of random graphs via the Glauber dynamics for the random-cluster model. The random-cluster model is parametrized by an edge probability p is an element of (0,1) and a cluster weight q > 0. We establish that for every q >= 1, the random-cluster Glauber dynamics mixes in optimal Theta(n log n) steps on n-vertex random graphs having a prescribed degree sequence with bounded average branc...
• RADNER EQUILIBRIUM AND SYSTEMS OF QUADRATIC BSDES WITH DISCONTINUOUS GENERATORS AI翻译
  作者：Escauriaza, Luis; Schwarz, Daniel C.; Xing, Hao
  作者单位：University of Basque Country; University of London; University College London; Boston University
  摘要：Motivated by an equilibrium problem, we establish the existence of a solution for a family of Markovian backward stochastic differential equations with quadratic nonlinearity and discontinuity in Z. Using unique continuation and backward uniqueness, we show that the set of discontinuity has measure zero. In a continuous-time stochastic model of an endowment economy, we prove the existence of an incomplete Radner equilibrium with nondegenerate endogenous volatility.
• SCALING LIMIT OF THE HOMOGENIZATION COMMUTATOR FOR GAUSSIAN COEFFICIENT FIELDS AI翻译
  作者：Duerinckx, Mitia; Fischer, Julian; Gloria, Antoine
  作者单位：Universite Libre de Bruxelles; Institute of Science & Technology - Austria; Sorbonne Universite; Universite Paris Cite
  摘要：Consider a linear elliptic partial differential equation in divergence form with a random coefficient field. The solution-operator displays fluctuations around its expectation. The recently-developed pathwise theory of fluctuations in stochastic homogenization reduces the characterization of these fluctuations to those of the so-called standard homogenization commutator. In this contribution, we investigate the scaling limit of this key quantity: starting from a Gaussian-like coefficient field...
• HYDRODYNAMIC LIMIT FOR A 2D INTERLACED PARTICLE PROCESS AI翻译
  作者：Lerouvillois, Vincent; Toninelli, Fabio
  作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Technische Universitat Wien
  摘要：The Markov dynamics of interlaced particle arrays, introduced by A. Borodin and P. L. Ferrari in (Comm. Math. Phys. 325 (2014) 603-684), is a classical example of (2 + 1)-dimensional random growth model belonging to the so-called Anisotropic KPZ universality class. In (Comm. Pure Appl. Math. 72 (2018) 620-666), a hydrodynamic limit-the convergence of the height profile, after space/time rescaling, to the solution of a deterministic Hamilton-Jacobi PDE with nonconvex Hamiltonian-was proven when...
• AN EFFICIENT ALGORITHM FOR SOLVING ELLIPTIC PROBLEMS ON PERCOLATION CLUSTERS AI翻译
  作者：Gu, Chenlin
  作者单位：Universite PSL; Ecole Normale Superieure (ENS)
  摘要：We present an efficient algorithm to solve elliptic Dirichlet problems defined on the cluster of supercritical Z(d)-Bernoulli percolation, as a generalization of the iterative method proposed by S. Armstrong, A. Hannukainen, T. Kuusi and J.-C. Mourrat (ESAIM Math. Model. Numer. Anal. (2021) 55 37-55). We also explore the two-scale expansion on the infinite cluster of percolation, and use it to give a rigorous analysis of the algorithm.
• BROADCASTING ON RANDOM RECURSIVE TREES AI翻译
  作者：Addario-Berry, Louigi; Devroye, Luc; Lugosi, Gabor; Velona, Vasiliki
  作者单位：McGill University; McGill University; ICREA; Pompeu Fabra University; Universitat Politecnica de Catalunya
  摘要：We study the broadcasting problem when the underlying tree is a random recursive tree. The root of the tree has a random bit value assigned. Every other vertex has the same bit value as its parent with probability 1 - q and the opposite value with probability q, where q is an element of [0, 1]. The broadcasting problem consists in estimating the value of the root bit upon observing the unlabeled tree, together with the bit value associated with every vertex. In a more difficult version of the ...
• CONSTRAINED STOCHASTIC LQ CONTROL WITH REGIME SWITCHING AND APPLICATION TO PORTFOLIO SELECTION AI翻译
  作者：Hu, Ying; Shi, Xiaomin; Xu, Zuo Quan
  作者单位：Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); Shandong University of Finance & Economics; Hong Kong Polytechnic University
  摘要：This paper is concerned with a stochastic linear-quadratic optimal control problem with regime switching, random coefficients and cone control constraint. The randomness of the coefficients comes from two aspects: the Brownian motion and the Markov chain. Using Ito's lemma for Markov chain, we obtain the optimal state feedback control and optimal cost value explicitly via two new systems of extended stochastic Riccati equations (ES-REs). We prove the existence and uniqueness of the two ESREs u...