Functional limit theorem for occupation times of Gaussian processes---non-critical case

Abstract

where X ^ X ^ , . . . are independent copies of X 7 . We shall consider only the case when fractional Brownian motion has jointly continuous local times which means the sample paths are point recurrent case, i.e., 0 2. Suppose f{x) > 0 be a bounded integrable function on M such that / := J R d f[χ)dx φ 0. We denote by lΊ^{t,x) the local time of fractional Brownian motion X 7 ' d , then putting a = 1 ηd,