The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 23, Number 6 (2013), 2472-2499.
A control problem with fuel constraint and Dawson–Watanabe superprocesses
We solve a class of control problems with fuel constraint by means of the log-Laplace transforms of $J$-functionals of Dawson–Watanabe superprocesses. This solution is related to the superprocess solution of quasilinear parabolic PDEs with singular terminal condition. For the probabilistic verification proof, we develop sharp bounds on the blow-up behavior of log-Laplace functionals of $J$-functionals, which might be of independent interest.
Ann. Appl. Probab., Volume 23, Number 6 (2013), 2472-2499.
First available in Project Euclid: 22 October 2013
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J85: Applications of branching processes [See also 92Dxx] 93E20: Optimal stochastic control
Secondary: 60H20: Stochastic integral equations 60H30: Applications of stochastic analysis (to PDE, etc.) 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)
Schied, Alexander. A control problem with fuel constraint and Dawson–Watanabe superprocesses. Ann. Appl. Probab. 23 (2013), no. 6, 2472--2499. doi:10.1214/12-AAP908. https://projecteuclid.org/euclid.aoap/1382447695