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Piecewise-deterministic processes and viscosity solutions. (English) Zbl 0917.93071
McEneaney, William M. (ed.) et al., Stochastic analysis, control, optimization and applications. A volume in honor of Wendell H. Fleming, on the occasion of his 70th birthday. Boston: Birkhäuser. 249-268 (1999).
It is proved that the value function of an optimal control problem with a piecewise deterministic process as underlying dynamics is the unique viscosity solution of the associated HJB equation.
For the entire collection see [Zbl 0905.00042].

MSC:
93E20 Optimal stochastic control
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
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