Distribution of the smallest visited point in a greedy walk on the line

2016 ◽  
Vol 53 (3) ◽  
pp. 880-887
Author(s):  
Katja Gabrysch
Keyword(s):  
Poisson Process ◽  
Real Line ◽  
Half Line ◽  
The Real ◽  
Independence Properties

AbstractWe consider a greedy walk on a Poisson process on the real line. It is known that the walk does not visit all points of the process. In this paper we first obtain some useful independence properties associated with this process which enable us to compute the distribution of the sequence of indices of visited points. Given that the walk tends to +∞, we find the distribution of the number of visited points in the negative half-line, as well as the distribution of the time at which the walk achieves its minimum.

scholarly journals The Wiener-Pitt Phenomenon on the Half-Line

1962 ◽  
Vol 13 (1) ◽  
pp. 37-38 ◽  
Author(s):  
J. H. Williamson
Keyword(s):  
Real Line ◽  
Half Line ◽  
Stieltjes Transform ◽  
The Real

It has been well known for many years (2) that if Fμ(t) is the Fourier-Stieltjes transform of a bounded measure μ on the real line R, which is bounded away from zero, it does not follow that [Fμ(t)]−1 is also the Fourier-Stieltjes transform of a measure. It seems of interest (as was remarked, in conversation, by J. D. Weston) to consider measures on the half-line R+ = [0, ∞[, instead of on R.

Dependent thinning of point processes

1980 ◽  
Vol 17 (04) ◽  
pp. 987-995 ◽  
Author(s):  
Valerie Isham
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Real Line ◽  
Point Processes ◽  
Compound Poisson Process ◽  
Second Order ◽  
Binary Variables ◽  
Compound Poisson ◽  
The Real ◽  
Markov Sequence

A point process, N, on the real line, is thinned using a k -dependent Markov sequence of binary variables, and is rescaled. Second-order properties of the thinned process are described when k = 1. For general k, convergence to a compound Poisson process is demonstrated.

Dependent thinning of point processes

1980 ◽  
Vol 17 (4) ◽  
pp. 987-995 ◽  
Author(s):  
Valerie Isham
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Real Line ◽  
Point Processes ◽  
Compound Poisson Process ◽  
Second Order ◽  
Binary Variables ◽  
Compound Poisson ◽  
The Real ◽  
Markov Sequence

A point process, N, on the real line, is thinned using a k -dependent Markov sequence of binary variables, and is rescaled. Second-order properties of the thinned process are described when k = 1. For general k, convergence to a compound Poisson process is demonstrated.

scholarly journals On the correlation between the volumes of the typical Poisson-Voronoi cell and the typical Stienen sphere

2007 ◽  
Vol 39 (04) ◽  
pp. 883-892
Author(s):  
Viktor Olsbo
Keyword(s):  
Poisson Process ◽  
Real Line ◽  
Integral Formula ◽  
Voronoi Cell ◽  
Random Set ◽  
Homogeneous Poisson Process ◽  
Analytical Expression ◽  
The Real ◽  
Typical Cell ◽  
Integral Formulae

In this paper we consider a tessellation V generated by a homogeneous Poisson process Φ in R d and, furthermore, the random set of spheres with centres being the points in Φ and having radii equal to half the distance to their closest neighbouring point in Φ. In R d we give an integral formula for the correlation between the volume of the typical cell and the volume of the sphere in the typical cell, and we also show that this correlation is strictly positive. Furthermore, on the real line we give an analytical expression for the correlation, and in the plane and in space we give simplified integral formulae. Numerical values for the correlation for d = 2,…,7 are also given.

scholarly journals Explicit Asymptotic Velocity of the Boundary between Particles and Antiparticles

2012 ◽  
Vol 2012 ◽  
pp. 1-32
Author(s):  
V. A. Malyshev ◽  
A. D. Manita ◽  
A. A. Zamyatin
Keyword(s):  
Infinite Number ◽  
Real Line ◽  
Large Time ◽  
Half Line ◽  
Large Time Asymptotics ◽  
Asymptotic Velocity ◽  
The Real ◽  
Time Asymptotics ◽  
Positive Half ◽  
Number Of Particles

On the real line initially there are infinite number of particles on the positive half line, each having one of -negative velocities . Similarly, there are infinite number of antiparticles on the negative half line, each having one of -positive velocities . Each particle moves with constant speed, initially prescribed to it. When particle and antiparticle collide, they both disappear. It is the only interaction in the system. We find explicitly the large time asymptotics of —the coordinate of the last collision before between particle and antiparticle.

scholarly journals Kolmogorov type inequalities for the Marchaud fractional derivatives on the real line and the half-line

2014 ◽  
Vol 2014 (1) ◽  
pp. 504 ◽  
Author(s):  
Vladislav F Babenko ◽  
Mariya S Churilova ◽  
Nataliia V Parfinovych ◽  
Dmytro S Skorokhodov
Keyword(s):  
Real Line ◽  
Fractional Derivatives ◽  
Half Line ◽  
Kolmogorov Type ◽  
The Real

scholarly journals On the correlation between the volumes of the typical Poisson-Voronoi cell and the typical Stienen sphere

2007 ◽  
Vol 39 (4) ◽  
pp. 883-892 ◽  
Author(s):  
Viktor Olsbo
Keyword(s):  
Poisson Process ◽  
Real Line ◽  
Integral Formula ◽  
Voronoi Cell ◽  
Random Set ◽  
Homogeneous Poisson Process ◽  
Analytical Expression ◽  
The Real ◽  
Typical Cell ◽  
Integral Formulae

In this paper we consider a tessellation V generated by a homogeneous Poisson process Φ in Rd and, furthermore, the random set of spheres with centres being the points in Φ and having radii equal to half the distance to their closest neighbouring point in Φ. In Rd we give an integral formula for the correlation between the volume of the typical cell and the volume of the sphere in the typical cell, and we also show that this correlation is strictly positive. Furthermore, on the real line we give an analytical expression for the correlation, and in the plane and in space we give simplified integral formulae. Numerical values for the correlation for d = 2,…,7 are also given.

The properties of Bessel-type fractional derivatives and integrals

2016 ◽  
pp. 3973-3982
Author(s):  
V. R. Lakshmi Gorty
Keyword(s):  
Fractional Order ◽  
Real Line ◽  
Computer Algebra System ◽  
Fractional Derivatives ◽  
Graphical Representation ◽  
Fractional Integrals ◽  
The Real ◽  
Fractional Derivatives And Integrals ◽  
Half Axis ◽  
Derivatives Of

The fractional integrals of Bessel-type Fractional Integrals from left-sided and right-sided integrals of fractional order is established on finite and infinite interval of the real-line, half axis and real axis. The Bessel-type fractional derivatives are also established. The properties of Fractional derivatives and integrals are studied. The fractional derivatives of Bessel-type of fractional order on finite of the real-line are studied by graphical representation. Results are direct output of the computer algebra system coded from MATLAB R2011b.

Sign in / Sign up

Export Citation Format

Share Document