@Article{JCM-42-1,
author = {Shounian, Deng and Fei, Chen and Weiyin, Fei and Xuerong, Mao},
title = {The Truncated EM Method for Jump-Diffusion SDDEs with Super-Linearly Growing Diffusion and Jump Coefficients},
journal = {Journal of Computational Mathematics},
year = {2024},
volume = {42},
number = {1},
pages = {178--216},
abstract = {<p style="text-align: justify;">This work is concerned with the convergence and stability of the truncated Euler-Maruyama (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 $(q &lt; 2)$ 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.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2204-m2021-0270},
url = {https://global-sci.com/article/84080/the-truncated-em-method-for-jump-diffusion-sddes-with-super-linearly-growing-diffusion-and-jump-coefficients}
}