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Additive control of stochastic linear systems with finite horizon. (English) Zbl 0587.93068

The authors consider an optimal stochastic control problem where the state of the system is a linear stochastic differential equation and the control acts additively on the state of the system. Assuming a special structure on the integral cost function to be minimized, the value function is characterized and simpler equivalent problems are derived.
Reviewer: P.L.Lions

MSC:

93E20 Optimal stochastic control
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
93C05 Linear systems in control theory
49J40 Variational inequalities
35K65 Degenerate parabolic equations
49L20 Dynamic programming in optimal control and differential games
35R35 Free boundary problems for PDEs
90C39 Dynamic programming
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