Hitting, returning and the short correlation function |
| |
Authors: | Miguel Abadi |
| |
Institution: | 1. IMECC, Universidade Estadual de Campinas, Cidade Universitária, P?a Sérgio Buarque de Holanda 651, Caixa Postal 6065, 13083-859, Campinas, SP, BRAZIL
|
| |
Abstract: | We consider a stochastic process with the weakest mixing condition: the so called α. For any fixed n-string we prove the following results. (1) The hitting time has approximately exponential law. (2) The return time has approximately
a convex combination between a Dirac measure at the origin and an exponential law. In both cases the parameter of the exponential
law is λ(A)ℙ(A) where ℙ(A) is the measure of the string and λ(A) is a certain autocorrelation function of the string. We show also that the weight of the convex combination is approximately
λ(A). We describe the behavior of this autocorrelation function. Our results hold when the rate of mixing decays polinomially
fast with power larger than the golden number. |
| |
Keywords: | Mixing recurrence rare event hitting time return time short correlation |
本文献已被 SpringerLink 等数据库收录! |
|