In this paper we develop necessary conditions for optimality, in the form of the Pontryagin maximum principle, for the optimal control problem of a class of infinite dimensional evolution equations with delay in the state. In the cost functional we allow the final cost to depend on the history of the state. To treat such kind of cost functionals we introduce a new form of anticipated backward stochastic differential equations which plays the role of dual equation associated to the control problem.

Guatteri, G., Masiero, F., & Orrieri, C. (2017). Stochastic Maximun Principle for SPDES with Delay. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 127(7), 2396-2427 [10.1016/j.spa.2016.11.007].

Stochastic Maximun Principle for SPDES with Delay

MASIERO, FEDERICA
Secondo
;
2017

Abstract

In this paper we develop necessary conditions for optimality, in the form of the Pontryagin maximum principle, for the optimal control problem of a class of infinite dimensional evolution equations with delay in the state. In the cost functional we allow the final cost to depend on the history of the state. To treat such kind of cost functionals we introduce a new form of anticipated backward stochastic differential equations which plays the role of dual equation associated to the control problem.
Articolo in rivista - Articolo scientifico
stochastic maximum principle, stochastic partial differential equations, anticipated backward stochastic differential equations
English
2396
2427
32
Accettato per la pubblicazione su Stochastic Processes and their Applications, disponibile on line il 7 Dicembre 2016
Guatteri, G., Masiero, F., & Orrieri, C. (2017). Stochastic Maximun Principle for SPDES with Delay. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 127(7), 2396-2427 [10.1016/j.spa.2016.11.007].
Guatteri, G; Masiero, F; Orrieri, C
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/137785
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