A control problem with fuel constraint and dawson-watanabe superprocesses

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. © Institute of Mathematical Statistics, 2013.