Randomized Milstein algorithm for approximation of solutions of jump-diffusion SDEs

被引：2
|
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 COMPUTATIONAL AND APPLIED MATHEMATICS | 2024年 / 440卷
基金：
奥地利科学基金会;
关键词：
Jump-diffusion SDEs; Randomized Milstein algorithm; Levy's area; n th minimal error; Optimality of algorithms; Information-based complexity; TIME-IRREGULAR COEFFICIENTS; INTEGRATION;
D O I：
10.1016/j.cam.2023.115631
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We investigate the error of the randomized Milstein algorithm for solving scalar jump- diffusion stochastic differential equations. We provide a complete error analysis under substantially weaker assumptions than those known in the literature. In case the jump-commutativity condition is satisfied, we prove optimality of the randomized Milstein algorithm by establishing matching lower bounds. Moreover, we give some insight into the multidimensional case by investigating the optimal convergence rate for the approximation of jump-diffusion type Levys' areas. Finally, we report numerical experiments that support our theoretical findings. (c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC
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页数：21
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