Parameter estimates for linear partial differential equations with fractional boundary noise. (English) Zbl 1154.60335

Maslowski, Bohdan; Pospíšil, Jan

Commun. Inf. Syst. 7, No. 1, 1-20 (2007).

Summary: Parameter-dependent linear evolution equations with a fractional noise in the boundary conditions are studied. Ergodic-type theorems for stationary and non-stationary solutions are verified and used to prove the strong consistency of a suitably defined family of estimators.

MSC:

60H15	Stochastic partial differential equations (aspects of stochastic analysis)
35R60	PDEs with randomness, stochastic partial differential equations
93E10	Estimation and detection in stochastic control theory

Keywords:

parameter identification; ergodicity; stochastic partial differential equations; fractional Brownian motion; fractional Ornstein-Uhlenbeck process