Matematiikan ja tilastotieteen laitoksen henkilökunta-alue

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Abstract: Integral representations of random variables are interesting subject of study and they are applied in different areas such as mathematical finance. It is known that any random variable can be represented as an Ito integral with respect to standard Brownian motion. Moreover, Mishura et al. (2013) showed that similar result holds true also for fractional Brownian motion with Hurst index H>1/2 if the integral is understood in a pathwise sense. In this talk we extend these result to cover a wide class of Gaussian processes. More precisely, we consider \alpha-Hölder continuous processes of order \alpha > 1/2 and, with some mild extra assumptions, we prove that any random variable can be represented as pathwise integral.




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