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

This paper is concerned with almost sure convergence of θ-EM scheme for neutral stochastic differential delay equations under local Lipschitz conditions with θ∈12,1. 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 logR.