Ergodicity and Parameter Estimates for Infinite-Dimensional Fractional Ornstein-Uhlenbeck Process

被引：0
作者：
Bohdan Maslowski
Jan Pospíšil
机构：
[1] Czech Academy of Sciences,Institute of Mathematics
[2] University of West Bohemia,Faculty of Applied Sciences, Department of Mathematics
来源：
Applied Mathematics and Optimization | 2008年 / 57卷
关键词：
Stochastic partial differential equations; Fractional Brownian motion; Fractional Ornstein-Uhlenbeck process; Strictly stationary solution; Ergodicity; Parameter estimates;
D O I：
暂无
中图分类号：
学科分类号：
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.
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页码：401 / 429
页数：28
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