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Maximum principle for optimal control of distributed parameter stochastic systems with random jumps. (English) Zbl 0811.49021

Elworthy, K.D. (ed.) et al., Differential equations, dynamical systems, and control science. A Festschrift in Honor of Lawrence Markus. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 152, 867-890 (1994).
The authors present a rather general Pontryagin-type maximum principle for an optimal stochastic control problem in Hilbert spaces. The states are governed by a stochastic differential equation with jump term, where drift, diffusion, and jump term may depend on the control, and the states have to satisfy an inclusion type end constraint. The functional to be minimized involves the end state as well as an integral of a function depending on state and control.
For the entire collection see [Zbl 0780.00045].

MSC:

49K45 Optimality conditions for problems involving randomness
49K27 Optimality conditions for problems in abstract spaces
93C25 Control/observation systems in abstract spaces
93E20 Optimal stochastic control
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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