Journal article
Adapted Integral Representations Of Random Variables
Year:
2015Published in:
International Journal of Modern Physics: Conference SeriesHölder processes
fractional Brownian motion
mixed fractional Brownian motion
pathwise integral
generalized Lebesgue–Stieltjes integral
integral representation
We study integral representations of random variables with respect to general Hölder continuous processes and with respect to two particular cases; fractional Brownian motion and mixed fractional Brownian motion. We prove that an arbitrary random variable can be represented as an improper integral, and that the stochastic integral can have any distribution. If in addition the random variable is a final value of an adapted Hölder continuous process, then it can be represented as a proper integral. It is also shown that in the particular case of mixed fractional Brownian motion, any adapted random variable can be represented as a proper integral.