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A Generalized Stochastic Process: Fractional G-Brownian Motion

Author

Listed:
  • Changhong Guo

    (Guangdong University of Technology)

  • Shaomei Fang

    (South China Agricultural University)

  • Yong He

    (Guangdong University of Technology)

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.

Suggested Citation

  • Changhong Guo & Shaomei Fang & Yong He, 2023. "A Generalized Stochastic Process: Fractional G-Brownian Motion," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-34, March.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-10010-9
    DOI: 10.1007/s11009-023-10010-9
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    References listed on IDEAS

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