The invariance principle for linear multi-parameter stochastic processes generated by associated fields

We derive the invariance principle for the linear random field generated by identically distributed and associated random fields. Our result extends the result in Bulinski and Keane [Bulinski, A.V., Keane, M.S., 1996. Invariance principle for associated random fields. J. Math. Sci. 81, 2905–2911.] to the linear random field in the identically distributed case as well as the result in Marinucci and Poghosyan [Marinucci, M., Poghosyan, S., 2001. Asymptotics for linear random fields. Probab. Lett. 51, 131–141.] to the associated case.