DeepAI AI Chat
Log In Sign Up

Explicit approximation of the invariant measure for SDDEs with the nonlinear diffusion term

03/10/2023
by   Li Xiaoyue, et al.
0

To our knowledge, the existing measure approximation theory requires the diffusion term of the stochastic delay differential equations (SDDEs) to be globally Lipschitz continuous. Our work is to develop a new explicit numerical method for SDDEs with the nonlinear diffusion term and establish the measure approximation theory. Precisely, we construct a function-valued explicit truncated Euler-Maruyama segment process (TEMSP) and prove that it admits a unique ergodic numerical invariant measure. We also prove that the numerical invariant measure converges to the underlying one of SDDE in the Fortet-Mourier distance. Finally, we give an example and numerical simulations to support our theory.

READ FULL TEXT

page 1

page 2

page 3

page 4

08/22/2022

An explicit approximation for super-linear stochastic functional differential equations

Since it is difficult to implement implicit schemes on the infinite-dime...
08/24/2023

Linear implicit approximations of invariant measures of semi-linear SDEs with non-globally Lipschitz coefficients

This article investigates the weak approximation towards the invariant m...
01/28/2021

Computer-assisted proofs for some nonlinear diffusion problems

In the last three decades, powerful computer-assisted techniques have be...