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Large deviations principle by viscosity solutions: the case of diffusions with oblique Lipschitz reflections

Magdalena Kobylanski (2013)

Annales de l'I.H.P. Probabilités et statistiques

We establish a Large Deviations Principle for diffusions with Lipschitz continuous oblique reflections on regular domains. The rate functional is given as the value function of a control problem and is proved to be good. The proof is based on a viscosity solution approach. The idea consists in interpreting the probabilities as the solutions to some PDEs, make the logarithmic transform, pass to the limit, and then identify the action functional as the solution of the limiting equation.

Le problème de Cauchy pour les équations de Hamilton-Jacobi-Bellman

Pierre-Louis Lions (1981)

Annales de la Faculté des sciences de Toulouse : Mathématiques

L'équation de Zakai et le problème séparé du contrôle optimal stochastique

Ulrich G. Haussmann (1985)

Séminaire de probabilités de Strasbourg

Limiting average cost control problems in a class of discrete-time stochastic systems

Nadine Hilgert, Onesimo Hernández-Lerma (2001)

Applicationes Mathematicae

We consider a class of $ℝ^{d}$ -valued stochastic control systems, with possibly unbounded costs. The systems evolve according to a discrete-time equation $x_{t + 1} = G ₙ (x_{t}, a_{t}) + ξ_{t}$ (t = 0,1,... ), for each fixed n = 0,1,..., where the $ξ_{t}$ are i.i.d. random vectors, and the Gₙ are given functions converging pointwise to some function $G_{\infty}$ as n → ∞. Under suitable hypotheses, our main results state the existence of stationary control policies that are expected average cost (EAC) optimal and sample path average cost (SPAC) optimal for...

Linear quadratic control. State space vs. polynomial equations

Vladimír Kučera (1983)

Kybernetika