Proposition 9.3.5.7. The convergence time to be close to the risk-sensitive payoff with error tolerance η is at most

$eq2838.jpg$

where (Gj)-1 is the inverse of the mapping $eq2839.jpg$ and $eq2840.jpg$, error = maxj errorj. In particular for gj = 1 (almost active case), the convergence time is of order of $eq2841.jpg$.

Proof. We verify that the solution of the ODE is $eq2842.jpg$. From the assumptions, the primitive function Gj is a bijection and $eq2843.jpg$. The last assertion is obtained for gj = 1. This completes the proof.

9.3.5.8    Explicit Solutions

As promised in our introduction of this Chapter, ...

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