Proposition 18.104.22.168. The convergence time to be close to the risk-sensitive payoff with error tolerance η is at most
where (Gj)-1 is the inverse of the mapping and , error = maxj errorj. In particular for gj = 1 (almost active case), the convergence time is of order of .
Proof. We verify that the solution of the ODE is . From the assumptions, the primitive function Gj is a bijection and . The last assertion is obtained for gj = 1. This completes the proof.
As promised in our introduction of this Chapter, ...