Bernoulli

  • Bernoulli
  • Volume 12, Number 3 (2006), 551-570.

The scaling limit behaviour of periodic stable-like processes

Rice Franke

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Abstract

We prove a functional non-central limit theorem for scaled Markov processes generated by pseudo-differential operators of periodic variable order. Two different situations occur. If the measure of the set where the order function attains its minimum αo is positive with respect to the invariant measure, the limit turns out to be an αo -stable Lévy process. In the other case the scaled sequence converges in probability to the zero function. The large deviation for this convergence is typical of processes having heavy-tail increments. It turns out that only a finite number of large jumps can be recovered on large scales. We also apply the results in order to understand the recurrence and transience of periodic stable-like processes.

Article information

Source
Bernoulli, Volume 12, Number 3 (2006), 551-570.

Dates
First available in Project Euclid: 28 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.bj/1151525136

Digital Object Identifier
doi:10.3150/bj/1151525136

Mathematical Reviews number (MathSciNet)
MR2232732

Zentralblatt MATH identifier
1114.60028

Keywords
functional non-central limit theorem homogenization stable-like process large deviations heavy-tail increment

Citation

Franke, Rice. The scaling limit behaviour of periodic stable-like processes. Bernoulli 12 (2006), no. 3, 551--570. doi:10.3150/bj/1151525136. https://projecteuclid.org/euclid.bj/1151525136


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