TY - JOUR
ID - 9921
TI - Preserving asymptotic mean-square stability of stochastic theta scheme for systems of stochastic delay differential equations
JO - Computational Methods for Differential Equations
JA - CMDE
LA - en
SN - 2345-3982
AU - Farkhondeh Rouz, Omid
AD - Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
Y1 - 2020
PY - 2020
VL - 8
IS - 3
SP - 468
EP - 479
KW - Stochastic delay differential equations
KW - Stochastic linear theta scheme
KW - Asymptotic mean-square stability
DO - 10.22034/cmde.2020.32139.1502
N2 - This article examines asymptotic mean-square stability analysis of stochastic linear theta (SLT) scheme for n-dimensional stochastic delay differential equations (SDDEs). We impose some conditions on drift and diffusion terms, which admit that the diffusion coefficient can be highly nonlinear and does not necessarily satisfy a linear growth or global Lipschitz condition. We prove that the proposed scheme is asymptotically mean square stable if the employed stepsize is smaller than a given and easily computable upper bound. In particular, based on our investigation in the case θ ∈[ 1/2 , 1], the stepsize is arbitrary. Eventually, numerical examples are given to demonstrate the effectiveness of our work.
UR - https://cmde.tabrizu.ac.ir/article_9921.html
L1 - https://cmde.tabrizu.ac.ir/article_9921_3f10a4526577f99bc18606248bc855b6.pdf
ER -