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Fokker–Planck type equations associated with fractional Brownian motion controlled by infinitely divisible processes

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  • Gajda, Janusz
  • Wyłomańska, Agnieszka

Abstract

In this paper we study the anomalous diffusion process driven by fractional Brownian motion delayed by general infinitely divisible subordinator. We show the analyzed process is the stochastic representation of the Fokker–Planck type equation that describes the probability density function of an introduced model. Moreover, we study main characteristics of the examined process, the first two moments, that allow us in special cases for classification of it as a system with accelerating-subdiffusion property.

Suggested Citation

  • Gajda, Janusz & Wyłomańska, Agnieszka, 2014. "Fokker–Planck type equations associated with fractional Brownian motion controlled by infinitely divisible processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 104-113.
    • Handle: RePEc:eee:phsmap:v:405:y:2014:i:c:p:104-113
    DOI: 10.1016/j.physa.2014.03.016
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    Cited by:

    1. Kumar, A. & Wyłomańska, A. & Połoczański, R. & Sundar, S., 2017. "Fractional Brownian motion time-changed by gamma and inverse gamma process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 648-667.
    2. Wang, Lu & Zhang, Rong & Yang, Lin & Su, Yang & Ma, Feng, 2018. "Pricing geometric Asian rainbow options under fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 8-16.
    3. Ahmadian, D. & Ballestra, L.V., 2020. "Pricing geometric Asian rainbow options under the mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    4. Vaidya, Tushar & Chotibut, Thiparat & Piliouras, Georgios, 2021. "Broken detailed balance and non-equilibrium dynamics in noisy social learning models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).

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