A Generalized Stochastic Process: Fractional G-Brownian Motion

Changhong Guo (), Shaomei Fang () and Yong He ()
Additional contact information
Changhong Guo: Guangdong University of Technology
Shaomei Fang: South China Agricultural University
Yong He: Guangdong University of Technology

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 1, 1-34

Abstract: Abstract 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.

Keywords: Fractional G-Brownian motion; G-expectation; Long-range dependence; Volatility uncertainty; Numerical simulation; 60G22; 60H05; 60H35 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-023-10010-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-10010-9

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-023-10010-9

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().