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

Journal Article · Sun Jun 15 00:00:00 EDT 2008 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-007-9028-3· OSTI ID:21242044

Maslowski, Bohdan ^[1]; Pospisil, Jan ^[2]

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1. Czech Academy of Sciences, Institute of Mathematics (Czech Republic)
2. University of West Bohemia, Faculty of Applied Sciences, Department of Mathematics (Czech Republic)

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.

• OSTI ID: 21242044
• Journal Information: Applied Mathematics and Optimization, Vol. 57, Issue 3; Other Information: DOI: 10.1007/s00245-007-9028-3; Copyright (c) 2008 Springer Science+Business Media, LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
BROWNIAN MOVEMENT
CYLINDRICAL CONFIGURATION
EQUATIONS
MATHEMATICAL EVOLUTION
MATHEMATICAL SOLUTIONS
STOCHASTIC PROCESSES