Compensator conditions for stochastic ordering of point processes

1991 ◽  
Vol 28 (4) ◽  
pp. 751-761 ◽  
Author(s):  
A. Kwieciński ◽  
R. Szekli
Keyword(s):  
Probability Space ◽  
Point Processes ◽  
Sufficient Conditions ◽  
Stochastic Ordering ◽  
Half Line ◽  
Simple Point ◽  
Martingale Approach ◽  
Random Elements ◽  
Markov Point Processes ◽  
Positive Half

Sufficient conditions are given under which two simple point processes on the positive half-line can be stochastically compared as random elements of D(0,∞) or R∞+ Using a martingale approach to point processes, the conditions are proposed via a compensator function family. Appropriate versions of the processes being compared are constructed on the same probability space. The results are illustrated by replacement policies and semi-Markov point processes.

Compensator conditions for stochastic ordering of point processes

1991 ◽  
Vol 28 (04) ◽  
pp. 751-761 ◽  
Author(s):  
A. Kwieciński ◽  
R. Szekli
Keyword(s):  
Probability Space ◽  
Point Processes ◽  
Sufficient Conditions ◽  
Stochastic Ordering ◽  
Half Line ◽  
Simple Point ◽  
Martingale Approach ◽  
Random Elements ◽  
Markov Point Processes ◽  
Positive Half

Sufficient conditions are given under which two simple point processes on the positive half-line can be stochastically compared as random elements of D(0,∞) or R∞ + Using a martingale approach to point processes, the conditions are proposed via a compensator function family. Appropriate versions of the processes being compared are constructed on the same probability space. The results are illustrated by replacement policies and semi-Markov point processes.

scholarly journals Invariant Bipartite Random Graphs on Rd

2014 ◽  
Vol 51 (3) ◽  
pp. 769-779
Author(s):  
Fabio Lopes
Keyword(s):  
Point Processes ◽  
Random Number ◽  
Probability Distributions ◽  
Sufficient Conditions ◽  
Stable Marriage ◽  
Simple Point ◽  
Stable Marriage Problem ◽  
Blue Point ◽  
Translation Invariant ◽  
Positive Integers

Suppose that red and blue points occur in Rd according to two simple point processes with finite intensities λR and λB, respectively. Furthermore, let ν and μ be two probability distributions on the strictly positive integers with means ν̅ and μ̅, respectively. Assign independently a random number of stubs (half-edges) to each red (blue) point with law ν (μ). We are interested in translation-invariant schemes for matching stubs between points of different colors in order to obtain random bipartite graphs in which each point has a prescribed degree distribution with law ν or μ depending on its color. For a large class of point processes, we show that such translation-invariant schemes matching almost surely all stubs are possible if and only if λRν̅ = λBμ̅, including the case when ν̅ = μ̅ = ∞ so that both sides are infinite. Furthermore, we study a particular scheme based on the Gale-Shapley stable marriage problem. For this scheme, we give sufficient conditions on ν and μ for the presence and absence of infinite components. These results are two-color versions of those obtained by Deijfen, Holroyd and Häggström.

scholarly journals Frames associated with shift invariant spaces on positive half line

2021 ◽  
Vol 13 (1) ◽  
pp. 23-44
Author(s):  
Owais Ahmad ◽  
Mobin Ahmad ◽  
Neyaz Ahmad
Keyword(s):  
Sufficient Conditions ◽  
Gabor Frames ◽  
Half Line ◽  
Necessary Condition ◽  
Wavelet Frames ◽  
Invariant Space ◽  
Unified Approach ◽  
Shift Invariant Spaces ◽  
Invariant Spaces ◽  
Positive Half

Abstract In this paper, we introduce the notion of Walsh shift-invariant space and present a unified approach to the study of shift-invariant systems to be frames in L2(ℝ+). We obtain a necessary condition and three sufficient conditions under which the Walsh shift-invariant systems constitute frames for L2(ℝ+). Furthermore, we discuss applications of our main results to obtain some known conclusions about the Gabor frames and wavelet frames on positive half line.

Some limit theorems for simple point processes (a martingale approach)

Stochastics ◽  
1980 ◽  
Vol 3 (1-4) ◽  
pp. 203-216 ◽  
Author(s):  
YU. M. Kabanov ◽  
R. SH Liptser ◽  
A. N Shiryaev
Keyword(s):  
Limit Theorems ◽  
Point Processes ◽  
Simple Point ◽  
Martingale Approach

scholarly journals Invariant Bipartite Random Graphs on Rd

2014 ◽  
Vol 51 (03) ◽  
pp. 769-779
Author(s):  
Fabio Lopes
Keyword(s):  
Point Processes ◽  
Random Number ◽  
Probability Distributions ◽  
Sufficient Conditions ◽  
Stable Marriage ◽  
Simple Point ◽  
Stable Marriage Problem ◽  
Blue Point ◽  
Translation Invariant ◽  
Positive Integers

Suppose that red and blue points occur inRdaccording to two simple point processes with finite intensities λRand λB, respectively. Furthermore, let ν and μ be two probability distributions on the strictly positive integers with means ν̅ and μ̅, respectively. Assign independently a random number of stubs (half-edges) to each red (blue) point with law ν (μ). We are interested in translation-invariant schemes for matching stubs between points of different colors in order to obtain random bipartite graphs in which each point has a prescribed degree distribution with law ν or μ depending on its color. For a large class of point processes, we show that such translation-invariant schemes matching almost surely all stubs are possible if and only if λRν̅ = λBμ̅, including the case when ν̅ = μ̅ = ∞ so that both sides are infinite. Furthermore, we study a particular scheme based on the Gale-Shapley stable marriage problem. For this scheme, we give sufficient conditions on ν and μ for the presence and absence of infinite components. These results are two-color versions of those obtained by Deijfen, Holroyd and Häggström.

scholarly journals Smoothness of topological equivalence on the half line for nonautonomous systems

2019 ◽  
Vol 150 (5) ◽  
pp. 2484-2502
Author(s):  
Álvaro Castañeda ◽  
Gonzalo Robledo ◽  
Pablo Monzón
Keyword(s):  
Sufficient Conditions ◽  
Half Line ◽  
Topological Equivalence ◽  
Asymptotically Stable ◽  
Nonautonomous Systems ◽  
Perturbed System ◽  
Continuity Properties ◽  
Differentiability Properties ◽  
Positive Half ◽  
Stable Linear

AbstractWe study the differentiability properties of the topological equivalence between a uniformly asymptotically stable linear nonautonomous system and a perturbed system with suitable nonlinearities. For this purpose, we construct a homeomorphism inspired in the Palmer's one restricted to the positive half line, studying additional continuity properties and providing sufficient conditions ensuring its Cr–smoothness.

scholarly journals Stochastic Comparisons of Some Distances between Random Variables

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 981
Author(s):  
Patricia Ortega-Jiménez ◽  
Miguel A. Sordo ◽  
Alfonso Suárez-Llorens
Keyword(s):  
Financial Risk ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Stochastic Ordering ◽  
Random Variable ◽  
Distribution Functions ◽  
Stochastic Comparisons ◽  
Stochastic Orderings ◽  
Absolute Value ◽  
The Difference

The aim of this paper is twofold. First, we show that the expectation of the absolute value of the difference between two copies, not necessarily independent, of a random variable is a measure of its variability in the sense of Bickel and Lehmann (1979). Moreover, if the two copies are negatively dependent through stochastic ordering, this measure is subadditive. The second purpose of this paper is to provide sufficient conditions for comparing several distances between pairs of random variables (with possibly different distribution functions) in terms of various stochastic orderings. Applications in actuarial and financial risk management are given.

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