UNIVERSITY
OF WROC£AW
 
Main Page
Contents
Online First
General Information
Instructions for authors


VOLUMES
44.1 43.2 43.1 42.2 42.1 41.2 41.1
40.2 40.1 39.2 39.1 38.2 38.1 37.2
37.1 36.2 36.1 35.2 35.1 34.2 34.1
33.2 33.1 32.2 32.1 31.2 31.1 30.2
30.1 29.2 29.1 28.2 28.1 27.2 27.1
26.2 26.1 25.2 25.1 24.2 24.1 23.2
23.1 22.2 22.1 21.2 21.1 20.2 20.1
19.2 19.1 18.2 18.1 17.2 17.1 16.2
16.1 15 14.2 14.1 13.2 13.1 12.2
12.1 11.2 11.1 10.2 10.1 9.2 9.1
8 7.2 7.1 6.2 6.1 5.2 5.1
4.2 4.1 3.2 3.1 2.2 2.1 1.2
1.1
 
 
WROC£AW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 18, Fasc. 1,
pages 39 - 81
 

LEVEL CROSSINGS AND LOCAL TIME FOR REGULARIZED GAUSSIAN PROCESSES

Corinne Berzin
José R. León
Joaquín Ortega

Abstract: Let (X ,t (- [0,1]) n be a centred stationary Gaussian process defined on (_O_,A,P ) with covariance function satisfying

r(t) ~ 1- C |t| 2a, 0 < a < 1, ast-- > 0.
Define the regularized process

Xe = fe * X and Ye = Xe/se, wheres2e = varXet,
fe is a kernel which approaches the Dirac delta function as e --> 0 and * denotes the convolution. We study the convergence of

integral oo [ Ye ] Ze(f) = e- a(a) N---(x)- LX(x) f(x)dx as e-- > 0, - oo c(e)
where N V(x) and LV(x) denote, respectively, the number of crossings and the local time at level x for the process V in [0,1] and

c(e) = (2var(Xet)/pvar(Xet))1/2.
The limit depends on the value of a.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

Download:    Abstract    Full text   Abstract + References