Maximum process problems in optimal control theory.
Peskir, Goran (2005)
Journal of Applied Mathematics and Stochastic Analysis
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Peskir, Goran (2005)
Journal of Applied Mathematics and Stochastic Analysis
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Vivek Borkar (2000)
Applicationes Mathematicae
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The problem of minimizing the ergodic or time-averaged cost for a controlled diffusion with partial observations can be recast as an equivalent control problem for the associated nonlinear filter. In analogy with the completely observed case, one may seek the value function for this problem as the vanishing discount limit of value functions for the associated discounted cost problems. This passage is justified here for the scalar case under a stability hypothesis, leading in particular...
Nicole El Karoui, Ioannis Karatzas (1989)
Séminaire de probabilités de Strasbourg
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Marina L. Kleptsyna, Alain Le Breton, Michel Viot (2008)
ESAIM: Probability and Statistics
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In this paper we solve the basic fractional analogue of the classical linear-quadratic Gaussian regulator problem in continuous-time with partial observation. For a controlled linear system where both the state and observation processes are driven by fractional Brownian motions, we describe explicitly the optimal control policy which minimizes a quadratic performance criterion. Actually, we show that a separation principle holds, , the optimal control separates into two stages based...
Jack, Andrew, Zervos, Mihail (2006)
Journal of Applied Mathematics and Stochastic Analysis
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Bahlali, Seid, Mezerdi, Brahim (2005)
Electronic Journal of Probability [electronic only]
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Runolfsson, Thordur (2000)
Mathematical Problems in Engineering
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Ocone, Daniel, Weerasinghe, Ananda (2003)
Electronic Journal of Probability [electronic only]
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Bahlali, Seïd, Mezerdi, Brahim, Djehiche, Boualem (2006)
Journal of Applied Mathematics and Stochastic Analysis
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Tyrone E. Duncan, B. Maslowski, B. Pasik-Duncan (2015)
Banach Center Publications
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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...