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

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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.

Publishing year

2007

Language

English

Pages

1457-1468

Publication/Series

International Mathematical Forum

Volume

2

Issue

30

Document type

Journal 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