@article{Zhu2024, 
author = {Yongxiang Zhu and Min Zhu},
title = {Well-posedness and order preservation for neutral type stochastic differential equations of infinite delay with jumps},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {5},
pages = {11537-11559},
keywords = {order preservation, infinite memory, neutral type stochastic differential equation, jump},
url = {https://www.sciopen.com/article/10.3934/math.2024566},
doi = {10.3934/math.2024566},
abstract = {In this work, we are concerned with the order preservation problem for multidimensional neutral type stochastic differential equations of infinite delay with jumps under non-Lipschitz conditions. By using a truncated Euler-Maruyama scheme and adopting an approximation argument, we have developed the well-posedness of solutions for a class of stochastic functional differential equations which allow the length of memory to be infinite, and the coefficients to be non-Lipschitz and even unbounded. Moreover, we have extended some existing conclusions on order preservation for stochastic systems to a more general case. A pair of examples have been constructed to demonstrate that the order preservation need not hold whenever the diffusion term contains a delay term, although the jump-diffusion coefficient could contain a delay term.}
}