Pathwise convergence of the Euler scheme for rough and stochastic differential equations

Autor:	Allan, Andrew L., Kwossek, Anna P., Liu, Chong, Prömel, David J.
Rok vydání:	2023
Předmět:	Mathematics - Probability Mathematics - Numerical Analysis 65C30 65L20 60H35 60L20
Druh dokumentu:	Working Paper
Popis:	The convergence of the first order Euler scheme and an approximative variant thereof, along with convergence rates, are established for rough differential equations driven by c\`adl\`ag paths satisfying a suitable criterion, namely the so-called Property (RIE), along time discretizations with vanishing mesh size. This property is then verified for almost all sample paths of Brownian motion, It\^o processes, L\'evy processes and general c\`adl\`ag semimartingales, as well as the driving signals of both mixed and rough stochastic differential equations, relative to various time discretizations. Consequently, we obtain pathwise convergence in p-variation of the Euler--Maruyama scheme for stochastic differential equations driven by these processes. Comment: 43 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.16489 Zobrazit plný text záznamu View this record from Arxiv