A CONTROL PROBLEM WITH FUEL CONSTRAINT AND DAWSON-WATANABE SUPERPROCESSES

• 成果类型: Article
• 署名作者: Schied, Alexander
• 署名单位: University of Mannheim
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/12-AAP908
• 发表日期: 2013
• 页码: 2472-2499
• 关键词: nonlinear differential-equations; super-brownian motion

摘要

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.