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.