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

In English

Författare

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.

Publiceringsår

2007

Språk

Engelska

Sidor

1457-1468

Publikation/Tidskrift/Serie

International Mathematical Forum

Volym

2

Issue

30

Dokumenttyp

Artikel i tidskrift

Förlag

Hikari Ltd

Ämne

  • Probability Theory and Statistics

Nyckelord

  • 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/Övrigt

  • ISSN: 1312-7594