This book presents the latest developments and progress in the numerical study of the stochastic functional differential equation, with a particular emphasis on the longtime asymptotics and probabilistic characteristics of numerical methods used to solve such equation. The longtime asymptotics under investigation include the time-independent convergence analysis in both the strong and weak senses, the numerical invariant measure, and the ergodicity of numerical methods. Additionally, the p...

The stochastic Maxwell equations play an essential role in many fields, including fluctuational electrodynamics, statistical radiophysics, integrated circuits, and stochastic inverse problems.This book provides some recent advances in the investigation of numerical approximations of the stochastic Maxwell equations via structure-preserving algorithms. It presents an accessible overview of the construction and analysis of structure-preserving algorithms with an emphasis on the prese...