TY - JOUR
T1 - Implicit numerical solutions to neutral-type stochastic systems with superlinearly growing coefficients
AU - Zhou, Shaobo
AU - Jin, Hai
N1 - Publisher Copyright:
© 2018 Elsevier B.V.
PY - 2019/4
Y1 - 2019/4
N2 - In this paper, our main aim is to investigate the stability and strong convergence of an implicit numerical approximations for neutral-type stochastic differential equations with superlinearly growing coefficients. After providing moment boundedness and exponential stability for the exact solutions, we show that the backward Euler–Maruyama numerical method preserves stability and boundedness of moments, and the numerical approximations converge strongly to the true solutions for sufficiently small step size.
AB - In this paper, our main aim is to investigate the stability and strong convergence of an implicit numerical approximations for neutral-type stochastic differential equations with superlinearly growing coefficients. After providing moment boundedness and exponential stability for the exact solutions, we show that the backward Euler–Maruyama numerical method preserves stability and boundedness of moments, and the numerical approximations converge strongly to the true solutions for sufficiently small step size.
KW - Backward Euler–Maruyama method
KW - Exponential stability
KW - Neutral-type stochastic differential equation
KW - Polynomial growth condition
KW - Strong convergence
UR - http://www.scopus.com/inward/record.url?scp=85056902029&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2018.10.029
DO - 10.1016/j.cam.2018.10.029
M3 - Article
AN - SCOPUS:85056902029
SN - 0377-0427
VL - 350
SP - 423
EP - 441
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
ER -