Ergodic boundary and point control for linear stochastic PDEs driven by a cylindrical Lévy process

Karel Kadlec; Bohdan Maslowski

doi:10.3934/dcdsb.2020137

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2020, Volume 25, Issue 10: 4039-4055. Doi: 10.3934/dcdsb.2020137

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Ergodic boundary and point control for linear stochastic PDEs driven by a cylindrical Lévy process

Karel Kadlec and
Bohdan Maslowski

Charles University, Prague, Faculty of Mathematics and Physics, Czech Republic

Received: July 2019

Revised: December 2019

Early access: April 2020

Published: October 2020

This research was supported by GAČR grant no. 19-07140S

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Abstract

An ergodic control problem is studied for controlled linear stochastic equations driven by cylindrical Lévy noise with unbounded control operator in a Hilbert space. A family of optimal controls is shown to consist of those asymptotically achieving the feedback form that employs the corresponding Riccati equation. The formula for optimal cost is given. The general results are applied to stochastic heat equation with boundary control and to stochastic structurally damped plate equations with point control.

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Mathematics Subject Classification: 60H15, 93E20.

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