On ergodic stochastic control
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
TypeArticle accepté pour publication ou publié
Journal nameCommunications in Partial Differential Equations
Taylor & Francis
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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 / Keywordsergodic optimal stochastic control problems
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