Interval estimations for Euler-Maruyama approximate solutions of stochastic differential equations with multiple delays

Abstract

Stochastic differential delay equations (SDDEs) are generalizations of stochastic differential equations (SDEs) because SDDEs may include information of the past process. SDDEs are used for describing models that the future states of systems depend on not only the present state but their past states. Solutions of SDDEs do not necessarily have the Markov property, and representations of the solutions are more complicated than those of SDEs. For this reason, approximate solutions of SDDEs have been studied. In this paper, we focus on error estimations of the Euler-Maruyama approximate solutions of SDDEs and consider confidence intervals for the approximate solutions.