an:02132212
Zbl 1074.65009
Gr??ne, Lars
Error estimation and adaptive discretization for the discrete stochastic Hamilton-Jacobi-Bellman equation
EN
Numer. Math. 99, No. 1, 85-112 (2004).
00111550
2004
j
65C30 60H15 60H35 49J55 65K10 49M25 65N15 49L20
stochastic optimal control; stochastic Hamilton-Jacobi-Bellman equation; a posteriori error estimates; feedback optimal control; numerical examples
The dynamic programming method is a well known technique for the numerical solution of optimal control problems. Generalizing the technique and results from the deterministic case [cf. the author, ibid. 75, 319--337 (1997; Zbl 0880.65045)], the author obtains a posteriori error estimates for the space discretization of the stochastic Hamilton-Jacobi-Bellman equation. This method gives full global information about the optimal value function of the related stochastic optimal control problem. Therefore a feedback optimal control can be obtained.
It is also demonstrated that the a posteriori error estimates are efficient and reliable for the numerical approximation of PDEs and they allow to derive a bound for the numerical error corresponding to the derivatives. The asymptotic behavior of the error estimates with respect to the size of the grid elements is also investigated. Finally, an adaptive space discretization scheme is developed and numerical examples are presented.
Viorel Arn??utu (Ia??i)
Zbl 0880.65045