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

Tyrone E. Duncan; B. Maslowski; B. Pasik-Duncan

Banach Center Publications (2015)

- Volume: 105, Issue: 1, page 91-102
- ISSN: 0137-6934

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topTyrone E. Duncan, B. Maslowski, and B. Pasik-Duncan. "Ergodic control of linear stochastic equations in a Hilbert space with fractional Brownian motion." Banach Center Publications 105.1 (2015): 91-102. <http://eudml.org/doc/282315>.

@article{TyroneE2015,

abstract = {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.},

author = {Tyrone E. Duncan, B. Maslowski, B. Pasik-Duncan},

journal = {Banach Center Publications},

keywords = {infinite-dimensional stochastic differential equations; fractional Brownian motion; optimal control; linear-quadratic problem},

language = {eng},

number = {1},

pages = {91-102},

title = {Ergodic control of linear stochastic equations in a Hilbert space with fractional Brownian motion},

url = {http://eudml.org/doc/282315},

volume = {105},

year = {2015},

}

TY - JOUR

AU - Tyrone E. Duncan

AU - B. Maslowski

AU - B. Pasik-Duncan

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

JO - Banach Center Publications

PY - 2015

VL - 105

IS - 1

SP - 91

EP - 102

AB - 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.

LA - eng

KW - infinite-dimensional stochastic differential equations; fractional Brownian motion; optimal control; linear-quadratic problem

UR - http://eudml.org/doc/282315

ER -

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