TY - UNPB
T1 - The backward Euler-Maruyama method for invariant measures of stochastic differential equations with super-linear coefficients
AU - Liu, Wei
AU - Mao, Xuerong
AU - Wu, Yue
PY - 2022/6/20
Y1 - 2022/6/20
N2 - The backward Euler-Maruyama (BEM) method is employed to approximate the invariant measure of stochastic differential equations, where both the drift and the diffusion coefficient are allowed to grow super-linearly. The existence and uniqueness of the invariant measure of the numerical solution generated by the BEM method are proved and the convergence of the numerical invariant measure to the underlying one is shown. Simulations are provided to illustrate the theoretical results and demonstrate the application of our results in the area of system control.
AB - The backward Euler-Maruyama (BEM) method is employed to approximate the invariant measure of stochastic differential equations, where both the drift and the diffusion coefficient are allowed to grow super-linearly. The existence and uniqueness of the invariant measure of the numerical solution generated by the BEM method are proved and the convergence of the numerical invariant measure to the underlying one is shown. Simulations are provided to illustrate the theoretical results and demonstrate the application of our results in the area of system control.
KW - stochastic differential equation
KW - stationary measure
KW - super-linear coefficients
KW - backward Euler-Maruyama method
UR - https://arxiv.org/abs/2206.09970
M3 - Working Paper/Preprint
BT - The backward Euler-Maruyama method for invariant measures of stochastic differential equations with super-linear coefficients
CY - Ithaca, New York
ER -