A higher-order approximation method for jump-diffusion SDEs with a discontinuous drift coefficient

被引：3

作者：

Przybylowicz, Pawel ^{[1
]}

Schwarz, Verena ^{[2
]}

Szoelgyenyi, Michaela ^{[2
]}

机构：

[1] AGH Univ Sci & Technol, Fac Appl Math, Al Mickiewicza 30, PL-30059 Krakow, Poland

[2] Univ Klagenfurt, Dept Stat, Univ Str 65-67, A-9020 Klagenfurt, Austria

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2024年 / 538卷 / 01期

基金：

奥地利科学基金会;

关键词：

equations; Discontinuous drift; Strong convergence rate; Jump -adapted scheme; Higher -order scheme; Jump-diffusion stochastic differential; STOCHASTIC DIFFERENTIAL-EQUATIONS; EULER-MARUYAMA SCHEME; STRONG-CONVERGENCE; MULTIDIMENSIONAL SDES; GLOBAL APPROXIMATION; BACKWARD EULER; STABILITY; DRIVEN; RATES;

D O I：

10.1016/j.jmaa.2024.128319

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present the first higher-order approximation scheme for solutions of jumpdiffusion stochastic differential equations with discontinuous drift. For this transformation-based jump-adapted quasi-Milstein scheme, we prove Lp-convergence order 3/4. To obtain this result, we prove that under slightly stronger assumptions (but still weaker than assumptions applied before) a related jump-adapted quasiMilstein scheme has convergence order 3/4; in a special case it even has convergence order 1. Order 3/4 is conjectured to be optimal. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).

引用

页数：46

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