It is well known that martingale difference sequences are very useful in applications and theory. On the other hand, the operator fractional Brownian motion as an extension of the well-known fractional Brownian motion also plays an important role in both applications and theory. In this paper, we study the relation between them. We construct an approximation sequence of operator fractional Brownian motion based on a martingale difference sequence.

This paper studies asymptotic behavior of solutions for the coupled nonlinear Schrödinger lattice system. We obtain the existence and stability of compact attractor by means of tail estimates method and finite-dimensional approximations.