The Annals of Applied Probability

最新文章

• A REVERSE ERGODIC THEOREM FOR INHOMOGENEOUS KILLED MARKOV CHAINS AND APPLICATION TO A NEW UNIQUENESS RESULT FOR REFLECTING DIFFUSIONS AI翻译
  作者：Costantini, Cristina; Kurtz, Thomas G.
  作者单位：G d'Annunzio University of Chieti-Pescara; G d'Annunzio University of Chieti-Pescara; University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
  摘要：Bass and Pardoux ( Probab. Theory Related Fields (1987) 76 557-572) deduce from the Krein-Rutman theorem a reverse ergodic theorem for a sub- probability transition function, which turns out to be a key tool in proving uniqueness of reflecting Brownian motion in cones in Kwon and Williams ( Trans. Amer. Math. Soc (1991) 32 739-780) and Taylor and Williams ( Probab. Theory Related Fields (1993) 96 283-317). By a different approach, we are able to prove an analogous reverse ergodic theorem for a...
• A FEASIBLE CENTRAL LIMIT THEOREM FOR REALISED COVARIATION OF SPDES IN THE CONTEXT OF FUNCTIONAL DATA AI翻译
  作者：Benth, Fred espen; Schroers, Dennis; Veraart, Almut e. d.
  作者单位：University of Oslo; Imperial College London
  摘要：This article establishes an asymptotic theory for volatility estimation in an infinite -dimensional setting. We consider mild solutions of semilinear stochastic partial differential equations and derive a stable central limit theorem for the semigroup-adjusted realised covariation (SARCV), which is a consistent estimator of the integrated volatility and a generalisation of the realised quadratic covariation to Hilbert spaces. Moreover, we introduce semigroup-adjusted multipower variations (SAM...
• SCALING LIMITS OF RANDOM WALKS, HARMONIC PROFILES, AND STATIONARY NONEQUILIBRIUM STATES IN LIPSCHITZ DOMAINS AI翻译
  作者：Dello Schiavo, Lorenzo; Portinale, Lorenzo; Sau, Federico
  作者单位：Institute of Science & Technology - Austria; University of Bonn; University of Catania
  摘要：We consider the open symmetric exclusion (SEP) and inclusion (SIP) processes on a bounded Lipschitz domain Omega, with both fast and slow boundary. For the random walks on Omega dual to SEP/SIP we establish: a functional-CLT-type convergence to the Brownian motion on Omega with either Neumann (slow boundary), Dirichlet (fast boundary), or Robin (at criticality) boundary conditions; the discrete-to-continuum convergence of the corresponding harmonic profiles. As a consequence, we rigorously der...
• DISTRIBUTION OF THE NUMBER OF PIVOTS NEEDED USING GAUSSIANELIMINATION WITH PARTIAL PIVOTING ON RANDOM MATRICES AI翻译
  作者：Peca-Medlin, John
  作者单位：University of Arizona
  摘要：Gaussian elimination with partial pivoting (GEPP) is a widely usedmethod to solve dense linear systems. Each GEPP step uses a row transposi-tion pivot movement if needed to ensure the leading pivot entry is maximalin magnitude for the leading column of the remaining untriangularized sub-system. We will use theoretical and numerical approaches to study how oftenthis pivot movement is needed. We provide full distributional descriptions forthe number of pivot movements needed using GEPP using par...
• DEFORMED SEMICIRCLE LAW AND CONCENTRATION OF NONLINEAR RANDOM MATRICES FOR ULTRA-WIDE NEURAL NETWORKS AI翻译
  作者：Wang, Zhichao; Zhu, Yizhe
  作者单位：University of California System; University of California San Diego; University of California System; University of California Irvine
  摘要：In this paper, we investigate a two -layer fully connected neural network of the form f (X) = 1/root d(1) a(T )sigma (W X ), where X is an element of (d0xn) is a deterministic data matrix, W is an element of R-d1xd0 and a is an element of R-d1 are random Gaussian weights, and sigma is a nonlinear activation function. We study the limiting spectral distributions of two empirical kernel matrices associated with f (X): the empirical conjugate kernel (CK) and neural tangent kernel (NTK), beyond th...
• THE JOINT FLUCTUATIONS OF THE LENGTHS OF THE Beta(2-α, α)-COALESCENTS AI翻译
  作者：Birkner, Matthias; Dahmer, Iulia; Diehl, Christina S.; Kersting, Goetz
  作者单位：Johannes Gutenberg University of Mainz; Goethe University Frankfurt
  摘要：We consider Beta(2 - alpha, alpha)-coalescents with parameter range 1 < alpha < 2 starting from n leaves. The length l(r)((n)) of order r in the n-Beta(2 - alpha, alpha)-coalescent tree is defined as the sum of the lengths of all branches that carry a subtree with r leaves. We show that for any s is an element of N the vector of suitably centered and rescaled lengths of orders 1 <= r <= s converges in distribution to a multivariate stable distribution as the number of leaves tends to infinity.
• PATHWISE LARGE DEVIATIONS FOR THE PURE JUMP k-NARY INTERACTING PARTICLE SYSTEMS AI翻译
  作者：Sun, Wen
  作者单位：Chinese Academy of Sciences; University of Science & Technology of China, CAS
  摘要：A pathwise large deviation result is proved for the pure jump models of the k-nary interacting particle system introduced by Kolokoltsov (Markov Process. Related Fields 12 (2006) 95-138; Nonlinear Markov Processes and Kinetic Equations (2010) Cambridge Univ. Press) that generalize classical Boltzmann's collision model, Smoluchovski's coagulation model and many others. The upper bound is obtained by following the standard methods (KOV (Comm. Pure Appl. Math. 42 (1989) 115-137)) of using a proce...
• CAUCHY PROBLEM OF STOCHASTIC KINETIC EQUATIONS AI翻译
  作者：Zhang, Xiaolong; Zhang, Xicheng
  作者单位：Beijing Institute of Technology
  摘要：In this paper we establish the optimal regularity estimates for the Cauchy problem of stochastic kinetic equations with random coefficients in anisotropic Besov spaces. As applications, we study the nonlinear filtering problem for a degenerate diffusion process, and obtain the existence and regularity of conditional probability densities under a few assumptions. Moreover, we also show the well-posedness for a class of super-linear growth stochastic kinetic equations driven by velocity-time whi...
• ASYMPTOTIC BEHAVIOUR OF THE NOISY VOTER MODEL DENSITY PROCESS AI翻译
  作者：Pymar, Richard; Rivera, Nicolas
  作者单位：University of London; University of Greenwich; Universidad de Valparaiso
  摘要：Given a transition matrix P indexed by a finite set V of vertices, the voter model is a discrete-time Markov chain in {0, 1}V where at each time-step a randomly chosen vertex x imitates the opinion of vertex y with probability P(x, y). The noisy voter model is a variation of the voter model in which vertices may change their opinions by the action of an external noise. The strength of this noise is measured by an extra parameter p is an element of [0, 1]. In this work we analyse the density pr...
• VISCOSITY SOLUTIONS TO SECOND ORDER ELLIPTIC HAMILTON-JACOBI-BELLMAN EQUATIONS WITH INFINITE DELAY AI翻译
  作者：Zhou, Jianjun
  作者单位：Northwest A&F University - China
  摘要：This paper introduces a notion of viscosity solutions for second order elated with infinite-horizon optimal control problems for stochastic differential equations with infinite delay. We identify the value functional of optimal control problems as unique viscosity solution to associated second order elliptic HJB equations with infinite delay. We also show that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions, and satisfies a stability property.