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

Aurélien Alfonsi (1, 2) , Vlad Bally (3, 1)

1 MATHRISK - Mathematical Risk Handling
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
3 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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: Random grids; Parametrix; Monte-Carlo methods; Approximation schemes

Domains: Probability [math.PR]

Aurélien Alfonsi, Vlad Bally. A generic construction for high order approximation schemes of semigroups using random grids. Numerische Mathematik, 2021, ⟨10.1007/s00211-021-01219-2⟩. ⟨hal-02406433⟩