Abstract
This article concerns the optimal control of piecewise deterministic processes in the viscosity solutions context. Boundary conditions given in Vermes (1985) are weakened and replaced by boundary conditions in exit-time optimal control problems as given in Barles (1994). It is proved that the value function of piecewise-deterministic process optimal control is the unique viscosity solution of its associated Hamilton-Jacobi-Bellman equation.
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Davis, M.H.A., Farid, M. (1999). Piecewise-Deterministic Processes and Viscosity Solutions. In: McEneaney, W.M., Yin, G.G., Zhang, Q. (eds) Stochastic Analysis, Control, Optimization and Applications. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1784-8_15
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DOI: https://doi.org/10.1007/978-1-4612-1784-8_15
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7281-6
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