A note on ergodic transformations of self-similar Volterra Gaussian processes

被引：7

作者：

Jost, Celine ^{[1
]}

机构：

[1] Univ Helsinki, Dept Math & Stat, FIN-00014 Helsinki, Finland

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2007年 / 12卷

关键词：

Volterra Gaussian process; self-similar process; ergodic transformation; fractional Brownian motion;

D O I：

10.1214/ECP.v12-1298

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We derive a class of ergodic transformations of self-similar Gaussian processes that are Volterra, i.e. of type X-t = integral(t)(0) z(X)(t, s) dW(s), t is an element of [0,infinity), where z(X) is a deterministic kernel and W is a standard Brownian motion.

引用

页码：259 / 266

页数：8

共 13 条

[1]

[Anonymous], THEORY PROBABILITY I

[2]

[Anonymous], 1993, TRANSLATIONS MATH MO

[3]

DEHEUVELS P, 1982, STOCHASTIC PROCESSES, V13, P311

[4]

Embrechts P, 2002, PRIN SER APPL MATH, P1

[5]

Erdelyi A., 1954, Tables of Integral Transforms

[6] STOCHASTIC AND MULTIPLE WIENER INTEGRALS FOR GAUSSIAN PROCESSES [J].

HUANG, ST ;

CAMBANIS, S .

ANNALS OF PROBABILITY, 1978, 6 (04) :585-614

[7]

JEULIN T, 1990, SEM PROB STRASB, V24, P227

[8]

JOST C, MEASURE PRESERVING T

[9] An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions [J].

Norros, I ;

Valkeila, E ;

Virtamo, J .

BERNOULLI, 1999, 5 (04) :571-587

[10] Explicit formulae for time-space Brownian chaos [J].

Peccati, G .

BERNOULLI, 2003, 9 (01) :25-48

← 1 2 →