THE TRUNCATED EM METHOD FOR JUMP-DIFFUSION SDDES WITH SUPER-LINEARLY GROWING DIFFUSION AND JUMP COEFFICIENTS  

作　　者：Shounian Deng Chen Fei Weiyin Fei Xuerong Mao 

机构地区：[1]Key Laboratory of Advanced Perception and Intelligent Control of High-end Equipment,Ministry of Education,and School of Mathematics-Physics and Finance,Anhui Polytechnic University,Wuhu 241000,China [2]Business School,University of Shanghai for Science and Technology,Shanghai 200093,China [3]Department of Mathematics and Statistics,University of Strathclyde,Glasgow G11XH,UK

出　　处：《Journal of Computational Mathematics》2024年第1期178-216,共39页计算数学（英文）

基　　金：the National Natural Science Foundation of China(62273003,12271003);the Open Project of Anhui Province Center for International Research of Intelligent Control of High-end Equipment(IRICHE-01);the Natural Science Foundation of Universities in Anhui Province(2022AH050993);the Startup Foundation for Introduction Talent of AHPU(2021YQQ058);the Royal Society(WM160014,Royal Society Wolfson Research Merit Award);the Royal Society and the Newton Fund(NA160317,Royal Society-Newton Advanced Fellowship);the Royal Society of Edinburgh(RSE1832)for their financial support.

摘　　要：This work is concerned with the convergence and stability of the truncated EulerMaruyama(EM)method for super-linear stochastic differential delay equations(SDDEs)with time-variable delay and Poisson jumps.By constructing appropriate truncated functions to control the super-linear growth of the original coefficients,we present two types of the truncated EM method for such jump-diffusion SDDEs with time-variable delay,which is proposed to be approximated by the value taken at the nearest grid points on the left of the delayed argument.The first type is proved to have a strong convergence order which is arbitrarily close to 1/2 in mean-square sense,under the Khasminskii-type,global monotonicity with U function and polynomial growth conditions.The second type is convergent in q-th(q<2)moment under the local Lipschitz plus generalized Khasminskii-type conditions.In addition,we show that the partially truncated EM method preserves the mean-square and H∞stabilities of the true solutions.Lastly,we carry out some numerical experiments to support the theoretical results.

关 键 词：SDDEs Truncated EM method Time-variable delay Poisson jumps 

分 类 号：O24[理学—计算数学]