Integral representation with adapted continuous integrand with respect\n to fractional Brownian motion

2014/03/09 by Georgiy Shevchenko, Lauri Viitasaari, Shevchenko, Georgiy +1
Economics, Econometrics and Finance · #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1403.2066

openalex publication_date 2014/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if a random variable is a final value of an adapted Holder\ncontinuous process, then it can be represented as a stochastic integral with\nrespect to fractional Brownian motion, and the integrand is an adapted process,\ncontinuous up to the final point.\n

Related

• Adapted integral representations of random variables
• Forward stochastic integration for adapted processes w.r.t. Riemann-Liouville fractional Brownian motion (Full version)
• On the fractional stochastic integration for random non-smooth integrands
• Fractional Brownian motion and the Markov Property
• Covariance of stochastic integrals with respect to fractional Brownian motion