Artículos de revistas
SELF-SIMILARITY AND LAMPERTI CONVERGENCE FOR FAMILIES OF STOCHASTIC PROCESSES
Fecha
2011Registro en:
LITHUANIAN MATHEMATICAL JOURNAL, v.51, n.3, p.342-361, 2011
0363-1672
Autor
JORGENSEN, Bent
MARTINEZ, Jose R.
DEMETRIO, Clarice G. B.
Institución
Resumen
We define a new type of self-similarity for one-parameter families of stochastic processes, which applies to certain important families of processes that are not self-similar in the conventional sense. This includes Hougaard Levy processes such as the Poisson processes, Brownian motions with drift and the inverse Gaussian processes, and some new fractional Hougaard motions defined as moving averages of Hougaard Levy process. Such families have many properties in common with ordinary self-similar processes, including the form of their covariance functions, and the fact that they appear as limits in a Lamperti-type limit theorem for families of stochastic processes.