On ergodic stochastic control

Arisawa, Mariko; Lions, Pierre-Louis

Arisawa, Mariko; Lions, Pierre-Louis (1998), On ergodic stochastic control, Communications in Partial Differential Equations, 23, 11-12, p. 333-358. http://dx.doi.org/10.1080/03605309808821413

Type

Article accepté pour publication ou publié

Date

1998

Journal name

Communications in Partial Differential Equations

Volume

Number

11-12

Publisher

Taylor & Francis

Pages

333-358

Abstract (EN)

We study here ergodic optimal stochastic control problems. After recalling some classical cases where the control system is known to be ergodic like the uniformly nondegenerate case or when there is an exactly controllable deterministic subsystem. we study new intermediate situations. We begin with the one-dimensional case that we essentially solve in full generality. We then consider the periodic case with constant coefficients and show that ergodicity is equivalent to some stochastic non resonance condition. Finally we show that the existence of one nondegenerate control is not sufficient for ergodicity. in dimensions larger than or equal to 2.

Subjects / Keywords

ergodic optimal stochastic control problems