Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-27T12:21:42.363Z Has data issue: false hasContentIssue false
  • English
  • Français

On a generalization of gamma processes

Published online by Cambridge University Press:  14 July 2016

Erhan Çinlar
Erhan Çinlar*
Affiliation:
Northwestern University
*
∗Postal address: Technological Institute, Room 1744, Northwestern University, Evanston IL 60201, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

We introduce a class of increasing processes with independent increments that reduce to gamma processes under the further condition of stationarity. Each such process can be reduced to a simple gamma process by a stochastic integral transformation. Applications to deformation laws of materials such as concrete are mentioned.

Keywords

GAMMA PROCESSESSTOCHASTIC TRANSFORMATIONSPROBABILITY LAWS FOR DEFORMATION OF MATERIALS
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 2 , June 1980 , pp. 467 - 480
Copyright
Copyright © Applied Probability Trust 1980 

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.)

Footnotes

Research supported by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant No. AFOSR–74–2733.

References

Bažant, Z. P. (1975) Theory of creep and shrinkage in concrete structures: A précis of recent developments. Mechanics Today 2, 1–191.Google Scholar
Choi, S. C. and Wette, R. (1969) Maximum likelihood estimation of the parameters of the gamma distribution and their bias. Technometrics 11, 683–690.Google Scholar
Çinlar, E. (1972) Superposition of point processes. In Stochastic Point Processes, ed. Lewis, P. A. W., Wiley, New York, 549–606.Google Scholar
Çinlar, E., Bažant, Z. P. and Osman, E. (1977) Stochastic process for extrapolating concrete creep. Journal of the Engineering Mechanics Division, Amer. Soc. Civil Engr. 103, No. EM6, 1069–1088.Google Scholar
Ito, K. (1969) Stochastic Processes. Aarhus Universitet Matematisk Institut, Lecture Notes Series No. 16.Google Scholar
Moran, P. A. P. (1957) The statistical treatment of flood flows. Trans. Amer. Geophysics Union 38, 519–523.Google Scholar