On a Voronoi aggregative process related to a bivariate Poisson process

1996 ◽  
Vol 28 (04) ◽  
pp. 965-981 ◽  
Author(s):  
S. G. Foss ◽  
S. A. Zuyev
Keyword(s):  
Asymptotic Behavior ◽  
Lower Bounds ◽  
Distribution Functions ◽  
Poisson Processes ◽  
Upper And Lower Bounds ◽  
Additive Functionals ◽  
Second Moments ◽  
Explicit Formulae ◽  
Bivariate Poisson Process ◽  
Sum Of Distances

We consider two independent homogeneous Poisson processes Π0 and Π1 in the plane with intensities λ0 and λ1, respectively. We study additive functionals of the set of Π0-particles within a typical Voronoi Π1-cell. We find the first and the second moments of these variables as well as upper and lower bounds on their distribution functions, implying an exponential asymptotic behavior of their tails. Explicit formulae are given for the number and the sum of distances from Π0-particles to the nucleus within a typical Voronoi Π1-cell.

On a Voronoi aggregative process related to a bivariate Poisson process

1996 ◽  
Vol 28 (4) ◽  
pp. 965-981 ◽  
Author(s):  
S. G. Foss ◽  
S. A. Zuyev
Keyword(s):  
Asymptotic Behavior ◽  
Lower Bounds ◽  
Distribution Functions ◽  
Poisson Processes ◽  
Upper And Lower Bounds ◽  
Additive Functionals ◽  
Second Moments ◽  
Explicit Formulae ◽  
Bivariate Poisson Process ◽  
Sum Of Distances

We consider two independent homogeneous Poisson processes Π0 and Π1 in the plane with intensities λ0 and λ1, respectively. We study additive functionals of the set of Π0-particles within a typical Voronoi Π1-cell. We find the first and the second moments of these variables as well as upper and lower bounds on their distribution functions, implying an exponential asymptotic behavior of their tails. Explicit formulae are given for the number and the sum of distances from Π0-particles to the nucleus within a typical Voronoi Π1-cell.

Approximations to hard-core models and their application to statistical analysis

1982 ◽  
Vol 19 (A) ◽  
pp. 281-292 ◽  
Author(s):  
Mark Westcott
Keyword(s):  
Statistical Analysis ◽  
Statistical Inference ◽  
Lower Bounds ◽  
Hard Core ◽  
Distribution Functions ◽  
Core Model ◽  
Upper And Lower Bounds ◽  
Nearest Neighbour ◽  
Hard Core Model

This paper derives upper and lower bounds to the distribution functions of nearest-neighbour and minimum nearest-neighbour distances between N points generated by a hard-core model on the surface of a sphere. The use of these bounds in statistical inference is discussed.

Approximations to hard-core models and their application to statistical analysis

1982 ◽  
Vol 19 (A) ◽  
pp. 281-292 ◽  
Author(s):  
Mark Westcott
Keyword(s):  
Statistical Analysis ◽  
Statistical Inference ◽  
Lower Bounds ◽  
Hard Core ◽  
Distribution Functions ◽  
Core Model ◽  
Upper And Lower Bounds ◽  
Nearest Neighbour ◽  
Hard Core Model

This paper derives upper and lower bounds to the distribution functions of nearest-neighbour and minimum nearest-neighbour distances between N points generated by a hard-core model on the surface of a sphere. The use of these bounds in statistical inference is discussed.

Bounds for the best constant in Landau/s inequality on the line

1983 ◽  
Vol 95 (3-4) ◽  
pp. 257-262 ◽  
Author(s):  
Z. M. Franco ◽  
Hans G. Kaper ◽  
Man Kam Kwong ◽  
A. Zettl
Keyword(s):  
Lower Bounds ◽  
Real Line ◽  
Upper Bound ◽  
Upper And Lower Bounds ◽  
Analyse Math ◽  
Best Constant ◽  
The Real ◽  
Explicit Formulae

SynopsisExplicit formulae and numerical values for upper and lower bounds for the best constant in Landau/s inequality on the real line are given. For p > 3, the value of the upper bound is less than the value of the best constant conjectured by Gindler and Goldstein (J. Analyse Math. 28 (1975), 213–238).

scholarly journals Dimer–monomer model on the Towers of Hanoi graphs

2015 ◽  
Vol 29 (23) ◽  
pp. 1550173 ◽  
Author(s):  
Hanlin Chen ◽  
Renfang Wu ◽  
Guihua Huang ◽  
Hanyuan Deng
Keyword(s):  
Asymptotic Behavior ◽  
Lower Bounds ◽  
Statistical Physics ◽  
Upper And Lower Bounds ◽  
Recursion Relations ◽  
Sierpiński Graphs ◽  
Towers Of Hanoi ◽  
The Difference ◽  
Significant Figures

The number of dimer–monomers (matchings) of a graph [Formula: see text] is an important graph parameter in statistical physics. Following recent research, we study the asymptotic behavior of the number of dimer–monomers [Formula: see text] on the Towers of Hanoi graphs and another variation of the Sierpiński graphs which is similar to the Towers of Hanoi graphs, and derive the recursion relations for the numbers of dimer–monomers. Upper and lower bounds for the entropy per site, defined as [Formula: see text], where [Formula: see text] is the number of vertices in a graph [Formula: see text], on these Sierpiński graphs are derived in terms of the numbers at a certain stage. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of the entropy can be evaluated with more than a hundred significant figures accuracy.

scholarly journals On the enumeration of column-convex permutominoes

2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
Nicholas R. Beaton ◽  
Filippo Disanto ◽  
Anthony J. Guttmann ◽  
Simone Rinaldi
Keyword(s):  
Functional Equation ◽  
Asymptotic Behavior ◽  
Numerical Analysis ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Recursive Construction ◽  
Nous Obtenons ◽  
Comportement Asymptotique ◽  
Generating Trees ◽  
International Audience

International audience We study the enumeration of \emphcolumn-convex permutominoes, i.e. column-convex polyominoes defined by a pair of permutations. We provide a direct recursive construction for the column-convex permutominoes of a given size, based on the application of the ECO method and generating trees, which leads to a functional equation. Then we obtain some upper and lower bounds for the number of column-convex permutominoes, and conjecture its asymptotic behavior using numerical analysis. Nous étudions l'énumeration des \emphpermutominos verticalement convexes, c.à.d. les polyominos verticalement convexes définis par un couple de permutations. Nous donnons une construction recursive directe pour ces permutominos de taille fixée, basée sur une application de la méthode ECO et les arbres de génération, qui nous amène à une équat ion fonctionelle. Ensuite nous obtenons des bornes superieures et inférieures pour le nombre de ces permutominos convexes et nous conjecturons leur comportement asymptotique à l'aide d'analyses numériques.

scholarly journals Asymptotic Behavior of Boson Regge Trajectories

2021 ◽  
Vol 66 (2) ◽  
pp. 97
Author(s):  
A.A. Trushevsky
Keyword(s):  
Asymptotic Behavior ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Square Root ◽  
Asymptotic Growth ◽  
Regge Trajectories ◽  
Phase Representation

The asymptotic behavior of boson Regge trajectories is studied. Upper and lower bounds on the asymptotic growth of the trajectories are obtained using the phase representation for the trajectories and a number of physical requirements. It is shown that, within the assumptions made, the asymptotic behavior of the trajectories is a square root.

COMPUTING BOUNDS ON RISK-NEUTRAL DISTRIBUTIONS FROM THE OBSERVED PRICES OF CALL OPTIONS

2010 ◽  
Vol 27 (02) ◽  
pp. 211-225
Author(s):  
MICHI NISHIHARA ◽  
MUTSUNORI YAGIURA ◽  
TOSHIHIDE IBARAKI
Keyword(s):  
Lower Bounds ◽  
Asset Price ◽  
Option Price ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Upper And Lower Bounds ◽  
Underlying Asset ◽  
No Arbitrage ◽  
Call Options ◽  
Risk Neutral

This paper derives, in closed forms, upper and lower bounds on risk-neutral cumulative distribution functions of the underlying asset price from the observed prices of European call options, based only on the no-arbitrage assumption. The computed bounds from the option price data show that the gap between the upper and lower bounds is large near the underlying asset price but gets smaller away from the underlying asset price. Since the bounds can be easily computed and visualized, they could be practically used by investors in various ways.

scholarly journals The Asymptotic Behavior of the Average $L^p-$Discrepancies and a Randomized Discrepancy

10.37236/378 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Stefan Steinerberger
Keyword(s):  
Asymptotic Behavior ◽  
Limit Theorem ◽  
Lower Bounds ◽  
Probabilistic Approach ◽  
Upper Bounds ◽  
Upper And Lower Bounds

This paper gives the limit of the average $L^p-$star and the average $L^p-$extreme discrepancy for $[0,1]^d$ and $0 < p < \infty$. This complements earlier results by Heinrich, Novak, Wasilkowski & Woźnia-kowski, Hinrichs & Novak and Gnewuch and proves that the hitherto best known upper bounds are optimal up to constants.We furthermore introduce a new discrepancy $D_{N}^{\mathbb{P}}$ by taking a probabilistic approach towards the extreme discrepancy $D_{N}$. We show that it can be interpreted as a centralized $L^1-$discrepancy $D_{N}^{(1)}$, provide upper and lower bounds and prove a limit theorem.

scholarly journals Bounds for eigenvalues of the Dirichlet problem for the logarithmic Laplacian

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Huyuan Chen ◽  
Laurent Véron
Keyword(s):  
Asymptotic Behavior ◽  
Fourier Transform ◽  
Dirichlet Problem ◽  
Lower Bounds ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Laplacian Operator ◽  
Lower And Upper Bounds

Abstract We provide bounds for the sequence of eigenvalues { λ i ⁢ ( Ω ) } i {\{\lambda_{i}(\Omega)\}_{i}} of the Dirichlet problem L Δ ⁢ u = λ ⁢ u ⁢  in  ⁢ Ω , u = 0 ⁢  in  ⁢ ℝ N ∖ Ω , L_{\Delta}u=\lambda u\text{ in }\Omega,\quad u=0\text{ in }\mathbb{R}^{N}% \setminus\Omega, where L Δ {L_{\Delta}} is the logarithmic Laplacian operator with Fourier transform symbol 2 ⁢ ln ⁡ | ζ | {2\ln\lvert\zeta\rvert} . The logarithmic Laplacian operator is not positively defined if the volume of the domain is large enough. In this article, we obtain the upper and lower bounds for the sum of the first k eigenvalues by extending the Li–Yau method and Kröger’s method, respectively. Moreover, we show the limit of the quotient of the sum of the first k eigenvalues by k ⁢ ln ⁡ k {k\ln k} is independent of the volume of the domain. Finally, we discuss the lower and upper bounds of the k-th principle eigenvalue, and the asymptotic behavior of the limit of eigenvalues.

Sign in / Sign up

Export Citation Format

Share Document