Bernoulli

  • Bernoulli
  • Volume 15, Number 1 (2009), 195-222.

Discrete approximation of a stable self-similar stationary increments process

C. Dombry and N. Guillotin-Plantard

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Abstract

The aim of this paper is to present a result of discrete approximation of some class of stable self-similar stationary increments processes. The properties of such processes were intensively investigated, but little is known about the context in which such processes can arise. To our knowledge, discretization and convergence theorems are available only in the case of stable Lévy motions and fractional Brownian motions. This paper yields new results in this direction. Our main result is the convergence of the random rewards schema first introduced by Cohen and Samorodnitsky, which we consider in a more general setting. Strong relationships with Kesten and Spitzer’s random walk in random sceneries are evidenced. Finally, we study some path properties of the limit process.

Article information

Source
Bernoulli, Volume 15, Number 1 (2009), 195-222.

Dates
First available in Project Euclid: 3 February 2009

Permanent link to this document
https://projecteuclid.org/euclid.bj/1233669888

Digital Object Identifier
doi:10.3150/08-BEJ147

Mathematical Reviews number (MathSciNet)
MR2546804

Zentralblatt MATH identifier
1214.60020

Keywords
random scenery random walk self-similarity stable process

Citation

Dombry, C.; Guillotin-Plantard, N. Discrete approximation of a stable self-similar stationary increments process. Bernoulli 15 (2009), no. 1, 195--222. doi:10.3150/08-BEJ147. https://projecteuclid.org/euclid.bj/1233669888


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References

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