Korean J. Math. Vol. 22 No. 1 (2014) pp.71-84
DOI: https://doi.org/10.11568/kjm.2014.22.1.71

# Weak convergence for multiple stochastic integrals in Skorohod space

## Abstract

By using the multidimensional normal approximation of functionals of Gaussian fields, we prove that functionals of Gaussian fields, as functions of $t$, converge weakly to a standard Brownian motion. As an application, we consider the convergence of the Stratonovich-type Riemann sums, as a function of $t$, of fractional Brownian motion with Hurst parameter $H=1/4$.

## Supporting Agencies

This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education Science and Technology (2012-012783).

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