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case1180979135.pdf (2.37 MB)
ETD Abstract Container
Abstract Header
Fractional Poisson Process in Terms of Alpha-Stable Densities
Author Info
Cahoy, Dexter Odchigue
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=case1180979135
Abstract Details
Year and Degree
2007, Doctor of Philosophy, Case Western Reserve University, Statistics.
Abstract
The link between fractional Poisson process (fPp) and α-stable density is established by solving an integral equation. The result is then used to study the properties of fPp such as asymptotical n-th arrival time, number of events distributions, covariance structure, stationarity and dependence of increments, self-similarity, and intermittency property. Asymptotically normal parameter estimators and their variants are derived; their properties are studied and compared using synthetic data. An alternative fPp model is also proposed.Finally, the asymptotic distribution of a scaled fPp random variable is shown to be free of some parameters; formulae for integer-order, non-central moments are also derived.
Committee
Wojbor Woyczynski (Advisor)
Subject Headings
Statistics
Keywords
fPp
;
N¿¿¿¿
;
POISSON PROCESS
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Citations
Cahoy, D. O. (2007).
Fractional Poisson Process in Terms of Alpha-Stable Densities
[Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1180979135
APA Style (7th edition)
Cahoy, Dexter.
Fractional Poisson Process in Terms of Alpha-Stable Densities.
2007. Case Western Reserve University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=case1180979135.
MLA Style (8th edition)
Cahoy, Dexter. "Fractional Poisson Process in Terms of Alpha-Stable Densities." Doctoral dissertation, Case Western Reserve University, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=case1180979135
Chicago Manual of Style (17th edition)
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Document number:
case1180979135
Download Count:
3,650
Copyright Info
© 2007, all rights reserved.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.