2014/04/29 by Georgiy Shevchenko, Lauri Viitasaari, Shevchenko, Georgiy +1
Economics, Econometrics and Finance · #60G15 #60G22 #60H05 #Complex Systems and Time Series Analysis #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1404.7518
openalex publication_date 2014/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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.