Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-05T16:04:39.193Z Has data issue: false hasContentIssue false
  • English
  • Français

On the dependence structure of hitting times of univariate processes

Published online by Cambridge University Press:  14 July 2016

Nader Ebrahimi  and
T. Ramalingam
Nader Ebrahimi*
Affiliation:
Northern Illinois University
T. Ramalingam*
Affiliation:
Northern Illinois University
*
∗Postal address: Division of Statistics, Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA.
∗Postal address: Division of Statistics, Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

Some concepts of dependence have recently been introduced by Ebrahimi (1987) to explore the structural properties of the hitting times of bivariate processes. In this framework, the special case of univariate processes has curious features. New properties are derived for this case. Some applications to sequential inference and inequalities for Brownian motion and new better than used (NBU) processes are also provided.

Keywords

PQDNQDPRDNRDTP2RR2BROWNIAN MOTIONNBU PROCESSSEQUENTIAL ESTIMATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 2 , June 1988 , pp. 355 - 362
Copyright
Copyright © Applied Probability Trust 1988 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ebrahimi, N. (1987) Bivariate processes with positive or negative dependent structures. J. Appl. Prob. 24, 115–122.CrossRefGoogle Scholar
Ebrahimi, N. and Ghosh, M. (1981) Multivariate negative dependence. Commun. Statist. A10, 307–337.Google Scholar
Friday, D. S. (1981) Dependence concepts for stochastic processes. Proc. Nato Advanced Study Institutes Series 5, 349–361.Google Scholar
Karlin, S. and Rinott, Y. (1980) Classes of orderings of measures and related correlation inequalities J. Multivariate Anal. 10, 467–498.CrossRefGoogle Scholar
Karlin, S. and Taylor, H. (1975) A First Course in Stochastic Processes. Academic Press, New York.Google Scholar
Karlin, S. and Taylor, H. (1981) A Second Course in Stochastic Processes. Academic Press, New York.Google Scholar
Keilson, J. (1971) Log-concavity and log-convexity in passage time densities of diffusion and birth and death processes. J. Appl. Prob. 8, 391–399.CrossRefGoogle Scholar
Knight, F. (1981) Essentials of Brownian Motion and Diffusion. American Mathematical Society, Providence, RI.CrossRefGoogle Scholar
Lehmann, E. L. (1966) Some concepts of dependence. Ann. Math. Statist. 37, 1136–1153.CrossRefGoogle Scholar
Leslie, R. T. (1969) Recurrence times of clusters of Poisson points. J. Appl. Prob. 6, 372–388.CrossRefGoogle Scholar
Marshall, A. and Shaked, M. (1983) New better than used processes. Adv. Appl. Prob. 15, 601–615.CrossRefGoogle Scholar
Ross, S. (1983) Stochastic Processes. Wiley, New York.Google Scholar
Shaked, M. (1982) A general theory of some positive dependence notions. J. Multivariate Anal. 12, 199–218.CrossRefGoogle Scholar
Sorensen, M. (1983) On maximum likelihood estimation in randomly stopped diffusion-type processes. Internat. Statist. Rev. 51, 93–110.CrossRefGoogle Scholar
Tong, Y. L. (1980) Probability Inequalities in Multivariate Distributions. Academic Press, New York.Google Scholar