Almost sure convergence rate of θ-EM scheme for neutral SDDEs

Abstract

This paper is concerned with almost sure convergence of θ -EM scheme for neutral stochastic differential delay equations under local Lipschitz conditions with θ ∈ 1 2 , 1 . It is revealed that the strong convergence rate under local Lipschitz condition is 1/2, while almost sure convergence rate is less than 1/2, provided the local Lipschitz constant, valid on balls of radius R , grows not faster than log R .