On the numerical approximation of an optimal correction problem. (English) Zbl 0661.65150

Bancora-Imbert, M. C.; Chow, P. L.; Menaldi, J. L.

SIAM J. Sci. Stat. Comput. 9, No. 6, 970-991 (1988).

Authors’ summary: The numerical solution of an optimal correction problem for a damped random linear oscillator is studied. A numerical algorithm for the discretized system of the associated dynamic programming equation is given. To initiate the computation, we adopt a numerical scheme derived from the deterministic version of the problem. Next, a correction-type algorithm based on a discrete maximum principle is introduced to ensure the convergence of the iteration procedure.

Reviewer: E.Platen

MSC:

65C99	Probabilistic methods, stochastic differential equations
65L05	Numerical methods for initial value problems involving ordinary differential equations
34F05	Ordinary differential equations and systems with randomness
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)

Keywords:

optimal correction; variational inequalities; free boundaries; damped random linear oscillator; dynamic programming; convergence; iteration