A Generalized dynamic programming principle and hamilton-jacobi-bellman equation
A Generalized dynamic programming principle and hamilton-jacobi-bellman equation
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DOI：
10.1080/17442509208833749
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发表时间：
1992-02
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影响因子：
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通讯作者：
S. Peng
中科院分区：
文献类型：
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作者：
S. Peng
我们将下面的完全非线性二阶偏微分方程解释为某个最优控制扩散问题的值函数，其中是一个以控制变量α ∈ A为参数的二阶椭圆型偏微分算子：其中σ，B，c是定义在上的函数，其值分别在中，是定义在上的真实的函数.这个等式的一个特例是。在这种情况下，方程是著名的Hamilton-Jacobi-Bellman方程。该问题的公式如下：控制问题的状态方程是一个经典的。代价函数由一个倒向随机微分方程的自适应解描述。本文讨论了这类问题的Bellman动态规划原理，证明了值函数是上述可能退化的完全非线性方程的粘性解
We interpret the following fully nonlinear second-order partial differential equation as the value function of a certain optimal controlled diffusion problem, where is a second order elliptic partial differential operator parametrized by the control variable αϵA: with Here σ,b, and c are functions defined on with values respectively in and is a real function defined on . A particular case of this equation is when . In this case, the equation is the well-known Hamilton-Jacobi-Bellman equation. The problem is formulated as follows: The state equation of the control problem is a classical one. The cost function is described by an adapted solution of a certain backward stochastic differential equation. The paper discusses Bellman's dynamic programming principle for this problem The value function is proved to be a viscosity solution of the above possibly degenerate fully nonlinear equation