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Invariance properties of the negative binomial Levy process and stochastic self-similarity.

Kozubowski, Tomasz and Podgorski, Krzysztof LU (2007) In International Mathematical Forum 2(30). p.1457-1468
Abstract
We study the concept of self-similarity with respect to stochastic

time change. The negative binomial process (NBP) is an example of a

family of random time transformations with respect to which stochastic

self-similarity holds for certain stochastic processes. These processes

include gamma process, geometric stable processes, Laplace motion, and

fractional Laplace motion. We derive invariance properties of the NBP

with respect to random time deformations in connection with stochastic

self-similarity. In particular, we obtain more general classes of processes

that exhibit stochastic self-similarity properties. As an application, our

results lead to... (More)
We study the concept of self-similarity with respect to stochastic

time change. The negative binomial process (NBP) is an example of a

family of random time transformations with respect to which stochastic

self-similarity holds for certain stochastic processes. These processes

include gamma process, geometric stable processes, Laplace motion, and

fractional Laplace motion. We derive invariance properties of the NBP

with respect to random time deformations in connection with stochastic

self-similarity. In particular, we obtain more general classes of processes

that exhibit stochastic self-similarity properties. As an application, our

results lead to approximations of the gamma process via the NBP and

simulation algorithms for both processes. (Less)
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organization
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Contribution to journal
publication status
published
subject
keywords
Compound Poisson process, Cox process, Discrete L´evy process, Doubly stochastic Poisson process, Fractional Laplace motion, Gamma- Poisson process, Gamma process, Geometric sum, Geometric distribution, Infinite divisibility, Point process, Random stability, Subordination, Self similarity, Simulation
in
International Mathematical Forum
volume
2
issue
30
pages
1457 - 1468
publisher
Hikari Ltd
ISSN
1312-7594
language
English
LU publication?
yes
id
803fe6de-d822-4d13-aa73-fc159b97046b (old id 3051929)
alternative location
http://www.m-hikari.com/imf-password2007/29-32-2007/kozubowskiIMF29-32-2007.pdf
date added to LUP
2012-09-11 13:23:14
date last changed
2016-04-16 05:14:30
@article{803fe6de-d822-4d13-aa73-fc159b97046b,
  abstract     = {We study the concept of self-similarity with respect to stochastic<br/><br>
time change. The negative binomial process (NBP) is an example of a<br/><br>
family of random time transformations with respect to which stochastic<br/><br>
self-similarity holds for certain stochastic processes. These processes<br/><br>
include gamma process, geometric stable processes, Laplace motion, and<br/><br>
fractional Laplace motion. We derive invariance properties of the NBP<br/><br>
with respect to random time deformations in connection with stochastic<br/><br>
self-similarity. In particular, we obtain more general classes of processes<br/><br>
that exhibit stochastic self-similarity properties. As an application, our<br/><br>
results lead to approximations of the gamma process via the NBP and<br/><br>
simulation algorithms for both processes.},
  author       = {Kozubowski, Tomasz and Podgorski, Krzysztof},
  issn         = {1312-7594},
  keyword      = {Compound Poisson process,Cox process,Discrete L´evy process,Doubly stochastic Poisson process,Fractional Laplace motion,Gamma- Poisson process,Gamma process,Geometric sum,Geometric distribution,Infinite divisibility,Point process,Random stability,Subordination,Self similarity,Simulation},
  language     = {eng},
  number       = {30},
  pages        = {1457--1468},
  publisher    = {Hikari Ltd},
  series       = {International Mathematical Forum},
  title        = {Invariance properties of the negative binomial Levy process and stochastic self-similarity.},
  volume       = {2},
  year         = {2007},
}