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
收藏
页码：259 / 266
页数：8
相关论文
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
    HUANG, ST
    CAMBANIS, S
    [J]. 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
    Norros, I
    Valkeila, E
    Virtamo, J
    [J]. BERNOULLI, 1999, 5 (04) : 571 - 587
  • [10] Explicit formulae for time-space Brownian chaos
    Peccati, G
    [J]. BERNOULLI, 2003, 9 (01) : 25 - 48
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