Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 20 February 2020Accepted: 29 June 2020Published online: 06 May 2021Keywordscubature, quadrature, quasi--Monte Carlo, randomized simulation-optimizationAMS Subject Headings65D32, 65C05Publication DataISSN (print): 0036-1445ISSN (online): 1095-7200Publisher: Society for Ind...

We show a Marcinkiewicz–Zygmund law of large numbers for jointly, dissociated exchangeable arrays, in L r ( ∈ 0 , 2 ) and almost surely. Then, we obtain iterated logarithm such arrays under weaker moment condition than the existing one.

An extensive literature in economics uses a continuum of random variables to model individual random shocks imposed on a large population. Let H denote the Hilbert space of square-integrable random variables. A key concern is to characterize the family of all H-valued functions that satisfy the law of large numbers when a large sample of agents is drawn at random. We use the iterative extension...

We prove two variants of Kolmogorov’s strong law of large numbers in a completely worst-case framework, eschewing any probabilistic assumptions. The first variant is an assertion about a game involving the Bookmaker predicting the values of unprobabilized random variables; in an intuitive sense it is much stronger than the usual strong law of large numbers for martingales. The second variant is...

The Linial–Meshulam complex model is a natural higher dimensional analog of the Erdős–Rényi graph model. In recent years, Linial and Peled established limit theorem for Betti numbers complexes with an appropriate scaling underlying parameter. present article aims to extend that result more general random simplicial models. We introduce class homogeneous spatially independent complexes, includin...

This note announces recent exciting progress on the frontier between algebraic topology and probability theory. It is intended for a journal which publishes such announcements (without an abstract, typically in Russian). A description of larger work included concluding remarks.

Pinsky (1996) [15] proved that the finite mass superdiffusion X corresponding to the semilinear operator Lu+ βu−αu exhibits local extinction if and only if λc ≤ 0, where λc := λc(L+β) is the generalized principal eigenvalue of L + β on R. For the case when λc > 0, it has been shown in Engländer and Turaev (2000) [8] that in law the superdiffusion locally behaves like exp[tλc] times a non-negati...

The importance and value of Jacob Bernoulli’s work was eloquently stated by Andrĕı Andreyevich Markov during a speech presented to the Russian Academy of Science on December 1, 1913. Marking the bicentennial anniversary of the Law of Large Numbers, Markov’s words remain pertinent one hundred years later: In concluding this speech, I return to Jacob Bernoulli. His biographers recall that, follow...