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Bernoulli Related Polynomials and Numbers [PDF]

Mathematics of Computation, 1979
The polynomials φ n ( x ; a , b ) {\varphi _n}(x;a,b) of degree n defined by the equations \[ Δ a φ n ( x
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Bernoulli track‐before‐detect smoothing for maritime radar

IET Radar, Sonar & Navigation, 2022
Detection and tracking of small targets in sea clutter using a high‐resolution radar is a challenging problem as the sea surface constantly moves in a complex manner, with rough seas creating strong target‐like returns. Recently, a Bernoulli track‐before‐
Branko Ristic, Robin Guan, Du Yong Kim, Luke Rosenberg   +3 more
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Some identities connecting Stirling numbers, central factorial numbers and higher-order Bernoulli polynomials

AIMS Mathematics
By utilizing the generating function of higher-order Bernoulli polynomials, we uncover novel relationships that intertwine higher-order Bernoulli polynomials, higher-order Bernoulli numbers, Stirling numbers of the second kind, and central factorial ...
Aimin Xu
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Fast Calculation of Bernoulli Numbers

Современные информационные технологии и IT-образование, 2019
Bernoulli numbers are often found in mathematical analysis, number theory, combinatorics, and other areas of mathematics. In some monographs on number theory there are separate chapters devoted only to Bernoulli numbers and their properties.
Rustem R. Aidagulov, Sergei T. Glavatsky
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BERNOULLI'S LAW OF LARGE NUMBERS [PDF]

ASTIN Bulletin, 2013
AbstractThis year we celebrate the 300th anniversary of Jakob Bernoulli's path-breaking work Ars conjectandi, which appeared in 1713, eight years after his death. In Part IV of his masterpiece, Bernoulli proves the law of large numbers which is one of the fundamental theorems in probability theory, statistics and actuarial science.
Bolthausen, Erwin, Wüthrich, Mario V
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Power series expansion, decreasing property, and concavity related to logarithm of normalized tail of power series expansion of cosine

Electronic Research Archive
In this paper, in view of a determinantal formula for higher order derivatives of the ratio of two differentiable functions, we expand the logarithm of the normalized tail of the power series expansion of the cosine function into a Maclaurin power series
Aying Wan, Feng Qi
doaj   +1 more source

Adaptive Multi-target Tracking Algorithm with Unknown Detection Probability [PDF]

Jisuanji gongcheng, 2017
In order to accurately model the system detection probability in a complex background,a Multi-Target Tracking(MTT) method with unknown detection probability is proposed.The detection probability is modeled by the Time Varying AutoRegressive(TVAR) process.
LIU Jun,YUAN Peiyan,QIU Hao
doaj   +1 more source

Local limit theorems via Landau-Kolmogorov inequalities

, 2015
In this article, we prove new inequalities between some common probability metrics. Using these inequalities, we obtain novel local limit theorems for the magnetization in the Curie-Weiss model at high temperature, the number of triangles and isolated ...
Ross, Nathan, Röllin, Adrian
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Robust Poisson Multi-Bernoulli Filter With Unknown Clutter Rate

IEEE Access, 2019
In Bayesian multi-target tracking (MTT), knowledge of clutter intensity is required for effective multi-target state estimation. In this paper, we propose an online multi-target filter that can operate under background with unknown clutter intensity. Our
Weijian Si, Hongfan Zhu, Zhiyu Qu
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Discretized normal approximation by Stein's method

, 2014
We prove a general theorem to bound the total variation distance between the distribution of an integer valued random variable of interest and an appropriate discretized normal distribution.
Fang, Xiao
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