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Fractional Brownian Motion Delayed by Tempered and Inverse Tempered Stable Subordinators

Author

Listed:
  • A. Kumar

    (Indian Institute of Technology Ropar)

  • J. Gajda

    (Wrocław University of Science and Technology)

  • A. Wyłomańska

    (Wrocław University of Science and Technology)

  • R. Połoczański

    (Wrocław University of Science and Technology)

Abstract

In recent years subordinated processes have been widely considered in the literature. These processes not only have wide applications but also have interesting theoretical properties. In this paper we consider fractional Brownian motion (FBM) time-changed by two processes, tempered stable and inverse tempered stable. We present main properties of the subordinated FBM such as long range dependence and associated fractional partial differential equations for the probability density functions. Moreover, we present how to simulate both subordinated processes.

Suggested Citation

  • A. Kumar & J. Gajda & A. Wyłomańska & R. Połoczański, 2019. "Fractional Brownian Motion Delayed by Tempered and Inverse Tempered Stable Subordinators," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 185-202, March.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:1:d:10.1007_s11009-018-9648-x
    DOI: 10.1007/s11009-018-9648-x
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    References listed on IDEAS

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    1. Kumar, A. & Vellaisamy, P., 2015. "Inverse tempered stable subordinators," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 134-141.
    2. Meerschaert, Mark M. & Scheffler, Hans-Peter, 2008. "Triangular array limits for continuous time random walks," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1606-1633, September.
    3. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    4. Sato, Ken-iti, 2001. "Subordination and self-decomposability," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 317-324, October.
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    2. Beghin, Luisa & Macci, Claudio & Ricciuti, Costantino, 2020. "Random time-change with inverses of multivariate subordinators: Governing equations and fractional dynamics," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6364-6387.

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