Fractional Brownian sheet and martingale difference random fields

Abstract

Abstract In this paper, we prove a functional central limit theorem for the multidimensional parameter fractional Brownian sheet using martingale difference random fields. The proof is based on the invariance principle for the Brownian sheet due Poghosyan and Roelly (Stat. Probab. Lett. 38:235-245, 1998).

Keywords

• martingale difference random fields
• multidimensional parameter fractional Brownian sheet
• weak convergence