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

共 50 条

[41] Approximation to the Dirichlet problem for a higher-order elliptic equation with a spectral parameter and a discontinuous nonlinearity
D. K. Potapov
Differential Equations, 2007, 43 : 1031 - 1032
[42] Approximation to the Dirichlet problem for a higher-order elliptic equation with a spectral parameter and a discontinuous nonlinearity
Potapov, D. K.
DIFFERENTIAL EQUATIONS, 2007, 43 (07) : 1031 - 1032
[43] A higher-order discontinuous enrichment method for the solution of high Peclet advection-diffusion problems on unstructured meshes
Farhat, C.
Kalashnikova, I.
Tezaur, R.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2010, 81 (05) : 604 - 636
[44] A higher order weak approximation of McKean–Vlasov type SDEs
Riu Naito
Toshihiro Yamada
BIT Numerical Mathematics, 2022, 62 : 521 - 559
[45] Range image segmentation by an effective jump-diffusion method
Han, F
Tu, ZW
Zhu, SC
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 2004, 26 (09) : 1138 - 1153
[46] JUMP-DIFFUSION APPROXIMATION OF STOCHASTIC REACTION DYNAMICS: ERROR BOUNDS AND ALGORITHMS
Ganguly, Arnab
Altintan, Derya
Koeppl, Heinz
MULTISCALE MODELING & SIMULATION, 2015, 13 (04): : 1390 - 1419
[47] A STRONG ORDER 1/2 METHOD FOR MULTIDIMENSIONAL SDES WITH DISCONTINUOUS DRIFT (vol 27, pg 2383, 2017)
Leobacher, Gunther
Szoelgyenyi, Michaela
ANNALS OF APPLIED PROBABILITY, 2019, 29 (05): : 3266 - 3269
[48] Higher-order jump conditions for conservation laws
Oksuzoglu, Hakan
THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS, 2018, 32 (04) : 399 - 409
[49] Higher-order jump conditions for conservation laws
Hakan Oksuzoglu
Theoretical and Computational Fluid Dynamics, 2018, 32 : 399 - 409
[50] A Double-ended Queue with Catastrophes and Repairs, and a Jump-diffusion Approximation
Antonio Di Crescenzo
Virginia Giorno
Balasubramanian Krishna Kumar
Amelia G. Nobile
Methodology and Computing in Applied Probability, 2012, 14 : 937 - 954

← 1 2 3 4 5 →