scholarly journals Stochastic orderings induced by star-shaped functions

1991 ◽  
Vol 14 (4) ◽  
pp. 639-664
Author(s):  
Henry A. Krieger
Keyword(s):  
Real Line ◽  
Stochastic Dominance ◽  
Joint Distribution ◽  
Decomposition Theorem ◽  
Open Interval ◽  
Distribution Functions ◽  
Proper Subset ◽  
Stochastic Orderings ◽  
The Real ◽  
Decreasing Functions

The non-decreasing functions whicl are star-shaped and supported above at each point of a non-empty closed proper subset of the real line induce an ordering, on the class of distribution functions with finite first moments, that is strictly weaker than first degree stochastic dominance and strictly stronger than second degree stochastic dominance. Several characterizations of this ordering are developed, both joint distribution criteria and those involving only marginals. Tle latter are deduced from a decomposition theorem, which reduces the problem to consideration of certain functions which are star-shaped on the complement of an open interval.

Some applications of renewal theory on the whole line

1970 ◽  
Vol 7 (03) ◽  
pp. 734-746
Author(s):  
Kenny S. Crump ◽  
David G. Hoel
Keyword(s):  
Distribution Function ◽  
Real Line ◽  
Renewal Theory ◽  
Open Interval ◽  
One Dimensional ◽  
The Real ◽  
Half Open Interval ◽  
Negative Function ◽  
Dimensional Distribution ◽  
Image Position

Suppose F is a one-dimensional distribution function, that is, a function from the real line to the real line that is right-continuous and non-decreasing. For any such function F we shall write F{I} = F(b)– F(a) where I is the half-open interval (a, b]. Denote the k-fold convolution of F with itself by Fk* and let Now if z is a non-negative function we may form the convolution although Z may be infinite for some (and possibly all) points.

On the Duality between Coalescing Brownian Motions

2005 ◽  
Vol 57 (1) ◽  
pp. 204-224 ◽  
Author(s):  
Jie Xiong ◽  
Xiaowen Zhou
Keyword(s):  
Brownian Motion ◽  
Real Line ◽  
Joint Distribution ◽  
High Density ◽  
Brownian Motions ◽  
Empirical Measures ◽  
The Real ◽  
Density Limit

AbstractA duality formula is found for coalescing Brownian motions on the real line. It is shown that the joint distribution of a coalescing Brownian motion can be determined by another coalescing Brownian motion running backward. This duality is used to study a measure-valued process arising as the high density limit of the empirical measures of coalescing Brownian motions.

On Fourier-Stieltjes Transforms

1955 ◽  
Vol 7 ◽  
pp. 453-461 ◽  
Author(s):  
A. P. Calderón ◽  
A. Devinatz
Keyword(s):  
Real Line ◽  
The Real ◽  
One To One ◽  
Image Position ◽  
Decreasing Functions ◽  
Stieltjes Transforms

Let be the class of bounded non-decreasing functions defined on the real line which are normalized by the conditions ϕ(− ∞) = 0 , ϕ(t + 0) = ϕ(t).Let be the class of Fourier-Stieltjes transforms of elements of i.e. the elements of and are connected by the relationwhere ϕ ∊ and Φ ∊ .It is well known, and easy to verify that this mapping from to is one to one (1, p. 67, Satz 18).

scholarly journals On convergence and compactness in variation with shift of discrete probability laws

2021 ◽  
Vol 8 (3) ◽  
pp. 385-393
Author(s):  
Ivan A. Alexeev ◽  
◽  
Alexey A. Khartov ◽  
Keyword(s):  
Real Line ◽  
Discrete Distribution ◽  
Distribution Functions ◽  
Divisible Distribution ◽  
Characteristic Functions ◽  
Infinitely Divisible Distribution ◽  
Infinitely Divisible ◽  
The Real ◽  
Convergence In Variation ◽  
Compactness Theorems

We consider a class of discrete distribution functions, whose characteristic functions are separated from zero, i. e. their absolute values are greater than positive constant on the real line. The class is rather wide, because it contains discrete infinitely divisible distribution functions, functions of lattice distributions, whose characteristic functions have no zeroes on the real line, and also distribution functions with a jump greater than 1/2. Recently the authors showed that characteristic functions of elements of this class admit the Lévy-Khinchine type representations with non-monotonic spectral function. Thus our class is included in the set of so called quasi-infinitely divisible distribution functions. Using these representation the authors also obtained limit and compactness theorems with convergence in variation for the sequences from this class. This note is devoted to similar results concerning convergence and compactness but with weakened convergence in variation. Replacing of type of convergence notably expands applicability of the results.

Some applications of renewal theory on the whole line

1970 ◽  
Vol 7 (3) ◽  
pp. 734-746
Author(s):  
Kenny S. Crump ◽  
David G. Hoel
Keyword(s):  
Distribution Function ◽  
Real Line ◽  
Renewal Theory ◽  
Open Interval ◽  
One Dimensional ◽  
The Real ◽  
Half Open Interval ◽  
Negative Function ◽  
Dimensional Distribution ◽  
Image Position

Suppose F is a one-dimensional distribution function, that is, a function from the real line to the real line that is right-continuous and non-decreasing. For any such function F we shall write F{I} = F(b)– F(a) where I is the half-open interval (a, b]. Denote the k-fold convolution of F with itself by Fk* and let Now if z is a non-negative function we may form the convolution although Z may be infinite for some (and possibly all) points.

scholarly journals On a theorem of Halmos concerning unbiased estimation of moments

1964 ◽  
Vol 4 (2) ◽  
pp. 229-232 ◽  
Author(s):  
H. S. Konijn
Keyword(s):  
Finite Number ◽  
Real Line ◽  
Borel Subset ◽  
Distribution Functions ◽  
Unbiased Estimation ◽  
The Real ◽  
Central Moments ◽  
Unbiased Estimates ◽  
First Moment

In [4] Halmos considers the following situation. Let be a class of distribution functions over a given (Borel) subset E of the real line, and F a function over . He investigates which functions F admit estimates that are unbiased over and what are all possible such estimates for any given F. In particular he shows that on the basis of a sample (of size n) one can always obtain an estimate of the first moment which is unbiased in and that the central moments Fm of order m ≧ 2 have estimates which are unbiased in if and only if n ≧ m, provided satisfies the following properties: Fm exists and is finite for all distributions in and includes all distributions which assign probability one to a finite number of points of E. Halmos also finds that symmetric estimates which are unbiased on are unique1 and have smaller variances on than unsymmetric unbiased estimates.

A Note on the Dirichlet Condition for Second-Order Differential Expressions

1976 ◽  
Vol 28 (2) ◽  
pp. 312-320 ◽  
Author(s):  
W. N. Everitt
Keyword(s):  
Differential Expression ◽  
Real Line ◽  
Open Interval ◽  
Dirichlet Condition ◽  
Second Order ◽  
The Real ◽  
Half Open Interval ◽  
Image Position ◽  
Complex Valued

Let M denote the formally symmetric, second-order differential expression given by, for suitably differentiable complex-valued functions ƒ,The coefficients p and q are real-valued, Lebesgue measurable on the halfclosed, half-open interval [a, b) of the real line, with - ∞ < a < b ≦ ∞, and satisfy the basic conditions:

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.

AN OSCILLATION FUNCTION ON THE REAL LINE

2000 ◽  
Vol 26 (1) ◽  
pp. 237
Author(s):  
Duszyński
Keyword(s):  
Real Line ◽  
The Real
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