On Large Deviations of Vector-Valued Additive Functions of a Markov Gaussian Field

2003 ◽  
Vol 43 (4) ◽  
pp. 389-400
Author(s):  
S. Čepulėnas
Keyword(s):  
Large Deviations ◽  
Gaussian Field ◽  
Additive Functions ◽  
Vector Valued

Decomposition of vector-valued additive functions

1992 ◽  
Vol 61 (1) ◽  
pp. 1926-1930
Author(s):  
V. N. Sudakov
Keyword(s):  
Additive Functions ◽  
Vector Valued

scholarly journals Large deviations of the limiting distribution in the Shanks–Rényi prime number race

2012 ◽  
Vol 153 (1) ◽  
pp. 147-166 ◽  
Author(s):  
YOUNESS LAMZOURI
Keyword(s):  
Asymptotic Behavior ◽  
Large Deviations ◽  
Prime Number ◽  
Riemann Hypothesis ◽  
Linear Independence ◽  
Limiting Distribution ◽  
Absolutely Continuous ◽  
Independence Hypothesis ◽  
Vector Valued Function ◽  
Vector Valued

AbstractLet q ≥ 3, 2 ≤ r ≤ φ(q) and a1, . . ., ar be distinct residue classes modulo q that are relatively prime to q. Assuming the Generalized Riemann Hypothesis (GRH) and the Linear Independence Hypothesis (LI), M. Rubinstein and P. Sarnak [11] showed that the vector-valued function Eq;a1, . . ., ar(x) = (E(x;q,a1), . . ., E(x;q,ar)), where $E(x;q,a)= ({\log x}/{\sqrt{x}})(\phi(q)\pi(x;q,a)-\pi(x))$, has a limiting distribution μq;a1, . . ., ar which is absolutely continuous on $\mathbb{R}^r$. Furthermore, they proved that for r fixed, μq;a1, . . ., ar tends to a multidimensional Gaussian as q → ∞. In the present paper, we determine the exact rate of this convergence, and investigate the asymptotic behavior of the large deviations of μq;a1, . . ., ar.

A Lebesgue Decomposition for Vector Valued Additive Set Functions Defined on a Lattice

1977 ◽  
Vol 29 (2) ◽  
pp. 295-298 ◽  
Author(s):  
Thomas P. Dence
Keyword(s):  
Abelian Group ◽  
Projection Operators ◽  
Additive Functions ◽  
Lebesgue Decomposition ◽  
Set Functions ◽  
Bounded Set ◽  
Vector Valued

Our aim is to establish the Lebesgue decomposition for s-bounded vector valued additive functions defined on lattices of sets in both the finitely and countably additive setting. Strongly bounded (s-bounded) set functions were first studied by Rickart [15], and then by Rao [14], Brooks [1] and Darst [5; 6]. In 1963 Darst [6] established a result giving the decomposition of s-bounded elements in a normed Abelian group with respect to an algebra of projection operators.

Stochastic simulation of the spatio-temporal field of the average daily heat index in Southern Russia

2020 ◽  
Vol 82 ◽  
pp. 149-160
Author(s):  
N Kargapolova
Keyword(s):  
Heat Waves ◽  
Numerical Models ◽  
Heat Index ◽  
Real Field ◽  
Gaussian Field ◽  
The Real ◽  
Southern Russia ◽  
Weather Stations ◽  
Spatio Temporal ◽  
Temporal Field

Numerical models of the heat index time series and spatio-temporal fields can be used for a variety of purposes, from the study of the dynamics of heat waves to projections of the influence of future climate on humans. To conduct these studies one must have efficient numerical models that successfully reproduce key features of the real weather processes. In this study, 2 numerical stochastic models of the spatio-temporal non-Gaussian field of the average daily heat index (ADHI) are considered. The field is simulated on an irregular grid determined by the location of weather stations. The first model is based on the method of the inverse distribution function. The second model is constructed using the normalization method. Real data collected at weather stations located in southern Russia are used to both determine the input parameters and to verify the proposed models. It is shown that the first model reproduces the properties of the real field of the ADHI more precisely compared to the second one, but the numerical implementation of the first model is significantly more time consuming. In the future, it is intended to transform the models presented to a numerical model of the conditional spatio-temporal field of the ADHI defined on a dense spatio-temporal grid and to use the model constructed for the stochastic forecasting of the heat index.

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