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

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Published: Mar 27, 2014
Mathematics Subject Classification:
60H07

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Yoon Tae Kim
Department of Finance and Information Statistics Hallym University

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 $H=1/4$.


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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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