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

Weak convergence for multiple stochastic integrals in Skorohod space

Yoon Tae Kim

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 $H=1/4$.

Subject classification

60H07

Sponsor(s)

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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