Krzysztof Podgórski
Head of the Department of Statistics, Professor
Invariance properties of the negative binomial Levy process and stochastic self-similarity.
Author
Summary, in English
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.
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.
Department/s
- Department of Statistics
Publishing year
2007
Language
English
Pages
1457-1468
Publication/Series
International Mathematical Forum
Volume
2
Issue
30
Document type
Article
Publisher
Hikari Ltd
Topic
- Probability Theory and Statistics
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
Status
Published
ISBN/ISSN/Other
- ISSN: 1312-7594