Weak Laws for the Increments of Wiener Processes, Brownian Bridges Empirical Processes and Partial Sums of I.I.D.R.V.’S

1987 ◽  
pp. 69-88 ◽  
Author(s):  
Paul Deheuvels ◽  
Pál Révész
Keyword(s):  
Empirical Processes ◽  
Partial Sums ◽  
Wiener Processes ◽  
Brownian Bridges ◽  
Weak Laws

A stochastic ordering of partial sums of independent random variables and of some random processes

1992 ◽  
Vol 29 (03) ◽  
pp. 645-654 ◽  
Author(s):  
Philip J. Boland ◽  
Frank Proschan ◽  
Y. L. Tong
Keyword(s):  
Random Variables ◽  
Stochastic Ordering ◽  
Random Processes ◽  
Reliability Theory ◽  
Independent Random Variables ◽  
Partial Sums ◽  
Similar Argument ◽  
First Passage ◽  
Wiener Processes ◽  
Likelihood Ratio Ordering

In this paper we first prove an arrangement-decreasing property of partial sums of independent random variables when they are partially ordered through the likelihood ratio ordering. We then apply a similar argument to obtain a stochastic ordering of random processes via a comparison of their parameter functions, with special applications to Poisson and Wiener processes. Finally, in Section 4 we present some applications in reliability theory, queueing, and first-passage problems.

Weakly Associated Random Variables

2019 ◽  
pp. 233-250
Author(s):  
Florence Merlevède ◽  
Magda Peligrad ◽  
Sergey Utev
Keyword(s):  
Asymptotic Behavior ◽  
Gaussian Processes ◽  
Random Variables ◽  
Empirical Processes ◽  
Partial Sums ◽  
Asymptotic Results ◽  
Associated Random Variables ◽  
Maximal Inequalities ◽  
Non Gaussian ◽  
Shed Light

The purposes of this chapter are to introduce the notion of weakly associated (negatively or positively) random variables and to develop tools that will allow us, in the chapters to follow, to give estimations of moments of partial sums, maximal inequalities, and asymptotic results with both Gaussian and non-gaussian limits. As we shall see, these results shed light on the asymptotic behavior of numerous examples such as exchangeable variables, certain Gaussian processes, empirical processes, various classes of Markov chains, and determinantal processes. They are also useful to study stochastic processes that are functionals of the two independent processes mentioned above.

A stochastic ordering of partial sums of independent random variables and of some random processes

1992 ◽  
Vol 29 (3) ◽  
pp. 645-654 ◽  
Author(s):  
Philip J. Boland ◽  
Frank Proschan ◽  
Y. L. Tong
Keyword(s):  
Random Variables ◽  
Stochastic Ordering ◽  
Random Processes ◽  
Reliability Theory ◽  
Independent Random Variables ◽  
Partial Sums ◽  
Similar Argument ◽  
First Passage ◽  
Wiener Processes ◽  
Likelihood Ratio Ordering

In this paper we first prove an arrangement-decreasing property of partial sums of independent random variables when they are partially ordered through the likelihood ratio ordering. We then apply a similar argument to obtain a stochastic ordering of random processes via a comparison of their parameter functions, with special applications to Poisson and Wiener processes. Finally, in Section 4 we present some applications in reliability theory, queueing, and first-passage problems.

Sign in / Sign up

Export Citation Format

Share Document