Drift-implicit Euler scheme for sandwiched processes driven by Hölder noises

2022/04/19 by Giulia Di Nunno, Di Nunno, Giulia, Yuliya Mishura +3
Economics, Econometrics and Finance · Social Sciences · #60G22 #60H10 #60H35 #91G30 #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2204.08827

openalex publication_date 2022/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we analyze the drift-implicit (or backward) Euler numerical scheme for a class of stochastic differential equations with unbounded drift driven by an arbitrary λ-Hölder continuous process, λ∈(0,1). We prove that, under some mild moment assumptions on the Hölder constant of the noise, the L^r(Ω;L^∞([0,T]))-rate of convergence is equal to λ. To exemplify, we consider numerical schemes for the generalized Cox--Ingersoll-Ross and Tsallis--Stariolo--Borland models. The results are illustrated by simulations.

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