Ergodic control of linear stochastic equations in a Hilbert space with fractional Brownian motion

• Autorzy: Tyrone E. Duncan , B. Maslowski , B. Pasik-Duncan
• Języki publikacji: EN

Abstrakty

EN

A linear-quadratic control problem with an infinite time horizon for some infinite dimensional controlled stochastic differential equations driven by a fractional Brownian motion is formulated and solved. The feedback form of the optimal control and the optimal cost are given explicitly. The optimal control is the sum of the well known linear feedback control for the associated infinite dimensional deterministic linear-quadratic control problem and a suitable prediction of the adjoint optimal system response to the future noise. Some examples of controlled stochastic partial differential equations that satisfy the problem formulation are given.

Kategorie tematyczne

• 60G15: Gaussian processes
• 60G22: Fractional processes, including fractional Brownian motion
• 93E20: Optimal stochastic control
• 60H15: Stochastic partial differential equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2015
• Tom: 105
• Numer: 1
• Strony: 91-102

Daty

wydano

2015

Twórcy

autor

Tyrone E. Duncan

• Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA

autor

B. Maslowski

• Charles University in Prague, Faculty of Mathematics and Physics, Sokolovska 83, 186 75 Prague 8, Czech Republic

autor

B. Pasik-Duncan

• Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA

Identyfikatory

DOI

10.4064/bc105-0-7