ABSTRACT
Jh(t , X, {a/}y = 07(n-T)) = h ^ f(Xj, cij) + M0(x„). (2.2) j =0
Let us consider now the value functions
r »->
{«,},=_m£_ C ,4 j h ^ f(xn ctj) + U0(x„)
if t > h, '■Uoix), if 0 < / < /!.
uh(t, x) =
(2.3)
(2.4)
PROPOSITION 2.1. (Discrete Dynamic Programming Principle). Let h > 0. The value function Uh satisfies
[f/fc] - | y/h] - 1 uh(t, x) = inf{«/} y=o (2.5)
for V s
Jt = p > 1.