## The Annals of Applied Probability

### A control problem with fuel constraint and Dawson–Watanabe superprocesses

Alexander Schied

#### Abstract

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.

#### Article information

Source
Ann. Appl. Probab., Volume 23, Number 6 (2013), 2472-2499.

Dates
First available in Project Euclid: 22 October 2013

https://projecteuclid.org/euclid.aoap/1382447695

Digital Object Identifier
doi:10.1214/12-AAP908

Mathematical Reviews number (MathSciNet)
MR3127942

Zentralblatt MATH identifier
1288.60100

#### Citation

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

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