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# A generic construction for high order approximation schemes of semigroups using random grids

1 MATHRISK - Mathematical Risk Handling
Inria de Paris, ENPC - École des Ponts ParisTech, UPEM - Université Paris-Est Marne-la-Vallée
Abstract : Our aim is to construct high order approximation schemes for general semigroups of linear operators $P_{t},t\geq 0$. In order to do it, we fix a time horizon $T$ and the discretization steps $h_{l}=\frac{T}{n^{l}},l\in \mathbb{N}$ and we suppose that we have at hand some short time approximation operators $Q_{l}$ such that $P_{h_{l}}=Q_{l}+O(h_{l}^{1+\alpha })$ for some $\alpha >0$. Then, we consider random time grids \$\Pi (\omega )=\{t_0(\omega )=0
Keywords :
Type de document :
Pré-publication, Document de travail
Domaine :

https://hal-enpc.archives-ouvertes.fr/hal-02406433
Contributeur : Aurélien Alfonsi <>
Soumis le : jeudi 12 décembre 2019 - 10:13:03
Dernière modification le : lundi 22 mars 2021 - 14:27:06

### Identifiants

• HAL Id : hal-02406433, version 1
• ARXIV : 1905.08548

### Citation

Aurélien Alfonsi, Vlad Bally. A generic construction for high order approximation schemes of semigroups using random grids. 2019. ⟨hal-02406433⟩

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