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arXiv · 1207.5809

A control problem with fuel constraint and Dawson-Watanabe superprocesses

Alexander Schied
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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.

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Alexander Schied. 2012-07-24. A control problem with fuel constraint and Dawson-Watanabe superprocesses. https://doi.org/10.1214/12-aap908

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