A Generalized Stochastic Process: Fractional G-Brownian Motion

In this paper, a new concept for some stochastic process called fractional G -Brownian motion (fGBm) is developed. The fGBm can exhibit long-range dependence and consider volatility uncertainty simultaneously, compared to the standard Brownian motion, fractional Brownian motion and G -Brownian motio...

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Bibliographic Details
Published in:Methodology and computing in applied probability 2023-03, Vol.25 (1), p.22, Article 22
Main Authors: Guo, Changhong, Fang, Shaomei, He, Yong
Format: Article
Language:English
Subjects:
Arbitrage
Brownian motion
Business and Management
Calculus
Economics
Electrical Engineering
Life Sciences
Mathematics and Statistics
Partial differential equations
Random variables
Randomness
Securities markets
Simulation
Statistics
Stochastic models
Stochastic processes
Volatility
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Summary:In this paper, a new concept for some stochastic process called fractional G -Brownian motion (fGBm) is developed. The fGBm can exhibit long-range dependence and consider volatility uncertainty simultaneously, compared to the standard Brownian motion, fractional Brownian motion and G -Brownian motion. Thus it generalizes the concepts of the latter three processes, and can be a better alternative stochastic process in real applications. The existence, representation and some intrinsic properties for the fGBm are discussed, and some partial differential equations related to fGBm are also present. Finally, some numerical simulations for the distributions of G -normally distributed random variable and sample paths of fGBm are carried out, which shows that fGBm can be better to describe the amplitudes of the randomness.
ISSN:1387-5841
1573-7713
DOI:10.1007/s11009-023-10010-9