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An Introduction To The Theory Of Point Processes

This paper considers a renewal process in which the interarrival times and rewards are characterized as fuzzy variables A fuzzy elementary renewal theorem shows that the expected number of renewals per unit time is just the expected reciprocal of the interarrival time Furthermore, the expected reward per unit time is provided by a fuzzy renewal reward theorem Finally, a numerical example is presented for illustrating the theorems introduced in the paper

Renewal process with fuzzy interarrival times and rewards

Random fuzzy renewal process

In this article, applying moment inequality of negatively dependent (ND) random variables which obtained by Asadian et al., the complete convergence theorem for weighted sums of arrays of rowwise ND random variables is discussed. As a result, the complete convergence theorem for ND arrays of random variables is extended. Our results generalize and improve those on complete convergence theorem previously obtained by Hu et al., Ahmed et al, Volodin, and Sung from the independent and identically distributed case to ND sequences. Mathematical Subject Classification: 62F12.

/pdf/a-complete-convergence-theorem-for-weighted-sums-of-arrays-5gpaaox9se.pdf

A complete convergence theorem for weighted sums of arrays of rowwise negatively dependent random variables

151 This section gives some fundamental definitions in the theory of probability, such as the definitions of a probability space and a random variable

The Strong Law of Large Numbers

1.Notation and auxiliary results.- 2.Maximal inequalities for multiple sums.- 3.Weak convergence of multiple sums.- 4.Weak law of large numbers for multiple sums.- 5.Almost sure convergence for multiple series.- 6.Boundedness of multiple series.- 7.Rate of convergence of multiple sums.- 8.Strong law of large numbers for independent non-identically distributed random variables.- 9.Strong law of large numbers for independent identically distributed random variables.- 10.Law of the iterated logarithm.- 11.Renewal theorem for random walks with multidimensional time.- 12.Existence of moments of the supremum of multiple sums and the strong law of large numbers.- 13.Complete convergence.

Limit Theorems for Multi-Indexed Sums of Random Variables

We study properties of a subclass of ORV functions introduced by Avakumovic and provide their applications for the strong law of large numbers for renewal processes.

Properties of a Subclass of Avakumović Functions and Their Generalized Inverses

http://uregina.ca/~volodin/OnTheAlmostSure.pdf

On the almost sure growth rate of sums of lower negatively dependent nonnegative random variables

Equivalences in strong limit theorems for renewal counting processes

/pdf/some-properties-of-asymptotic-quasi-inverse-functions-and-443m63wsqk.pdf

Oleg I. Klesov

Papers

Limit Theorems for Multi-Indexed Sums of Random Variables

Properties of a Subclass of Avakumović Functions and Their Generalized Inverses

On the almost sure growth rate of sums of lower negatively dependent nonnegative random variables

Equivalences in strong limit theorems for renewal counting processes

Some properties of asymptotic quasi-inverse functions and their applications I