Invariance properties of the negative binomial Levy process and stochastic self-similarity.
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3051929
- author
- Kozubowski, Tomasz and Podgorski, Krzysztof LU
- organization
- publishing date
- 2007
- type
- 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
- 2016-04-01 17:01:31
- date last changed
- 2018-11-21 20:46:03
@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}},
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}},
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.}},
url = {{http://www.m-hikari.com/imf-password2007/29-32-2007/kozubowskiIMF29-32-2007.pdf}},
volume = {{2}},
year = {{2007}},
}