Convergence of stochastic numerical methods: from simulation to theory

Convergence of stochastic numerical methods: from simulation to theory

As an introduction, I will recall why convergence of stochastic numerical methods usually suffers from bad regularity of the noise, and the difficulty to exhibit speed of convergence or high order schemes, contrary to the deterministic case. Next, I will present some new stochastic schemes coming from usual numerical simulations and I will try to recover the theoretical order illustrated by stochastic sampling, proving higher order of convergence than the expected order in deterministic case. Finally, after "thèse" and "anti-thèse", there will be "synthèse".

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