A Semi-linear Backward Parabolic Cauchy Problem with Unbounded Coefficients of Hamilton-Jacobi-Bellman Type and Applications to Optimal Control

被引:2
作者
Addona, Davide [1 ]
机构
[1] Univ Milano Bicocca, MILANO BICOCCA Dipartimento Matemat, I-20155 Milan, Italy
关键词
Semi-linear parabolic equations; Weighted gradient uniform estimates; Unbounded coefficients; Hamilton-Jacobi-Bellman equation; Forward-backward stochastic differential equations; Stochastic optimal control; STOCHASTIC DIFFERENTIAL-EQUATIONS; KOLMOGOROV EQUATIONS; OPERATORS; SPACES;
D O I
10.1007/s00245-014-9270-4
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We obtain weighted uniform estimates for the gradient of the solutions to a class of linear parabolic Cauchy problems with unbounded coefficients. Such estimates are then used to prove existence and uniqueness of the mild solution to a semi-linear backward parabolic Cauchy problem, where the differential equation is the Hamilton-Jacobi-Bellman equation of a suitable optimal control problem. Via backward stochastic differential equations, we show that the mild solution is indeed the value function of the controlled equation and that the feedback law is verified.
引用
收藏
页码:1 / 36
页数:36
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