We introduce a generalized mixed fractional Brownian motion (gmfBm) as a linear combination of n independent fractional Brownian motions with possibly different Hurst indices and investigate conditions under which the time-changed gmfBm exhibit long-range dependence when the time-change is induced by a tempered stable subordinator or a Gamma process.
Prakasa RaoBLS.Option pricing for processes driven by mixed fractional Brownian motion with superimposed jumps. Probab Eng Inform Sc2015, 29, 589–596.
3.
Prakasa RaoBLS.Pricing geometric Asian power options under mixed fractional Brownian motion environment. Phys A: Stat Mech Appl2015, 446, 92–99.
4.
MishuraY.Stochastic calculus for fractional Brownian motion and related processes. Springer2008.
5.
Prakasa RaoBLS.Statistical Inference for fractional diffusion processes. Wiley2010.
6.
Prakasa RaoBLS.Fractional processes and their statistical inference: an overview. Jl of IISc2022, 102, 1145–1175.
7.
KumarA, GajdaG and WylomanskaA.Fractional Brownian motion delayed by tempered and inverse tempered stable subordinators. Methodol Comput Appl Probab2019; 21: 185–202.
8.
KumarA, WylomanskaA, PolozanskiR, . Fractional Brownian motion time-changed by gamma and inverse gamma process. Phys A: Stat Mech Appl2017; 468: 648–667.
9.
AlajmiS and MilkiE.On the mixed fractional Brownian motion time changed by inverse α-stable subordinator. Appl Math Sci2020; 14: 755–763.
10.
AlajmiS and MilkiE.On the long range dependence of time-changed mixed fractional Brownian motion model. 2021. arXiv:2102.10180v1 [math.PR] 18 Feb 2021.