Ergodicity and parameter estimates for infinite-dimensional fractional Ornstein-Uhlenbeck process

被引：28

作者：

Maslowski, Bohdan ^{[1
]}

Pospisil, Jan ^{[2
]}

机构：

[1] Acad Sci Czech Republ, Inst Math, CR-11567 Prague 1, Czech Republic

[2] Univ W Bohemia, Dept Math, Fac Sci Appl, Plzen 30614, Czech Republic

来源：

APPLIED MATHEMATICS AND OPTIMIZATION | 2008年 / 57卷 / 03期

关键词：

stochastic partial differential equations; fractional Brownian motion; fractional Ornstein-Uhlenbeck process; strictly stationary solution; ergodicity; parameter estimates;

D O I：

10.1007/s00245-007-9028-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Existence and ergodicity of a strictly stationary solution for linear stochastic evolution equations driven by cylindrical fractional Brownian motion are proved. Ergodic behavior of non-stationary infinite-dimensional fractional Ornstein-Uhlenbeck processes is also studied. Based on these results, strong consistency of suitably defined families of parameter estimators is shown. The general results are applied to linear parabolic and hyperbolic equations perturbed by a fractional noise.

引用

页码：401 / 429

页数：29

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