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Stable Processes with Stationary Increments Parameterized by Metric Spaces

Author

Listed:
  • Zuopeng Fu

    (University of Cincinnati)

  • Yizao Wang

    (University of Cincinnati)

Abstract

A new family of stable processes indexed by metric spaces with stationary increments is introduced. They are special cases of a new family of set-indexed stable processes with Chentsov representation. At the heart of the representation, a result on the so-called measure definite kernels is of independent interest. A limit theorem for set-indexed processes is also established.

Suggested Citation

  • Zuopeng Fu & Yizao Wang, 2020. "Stable Processes with Stationary Increments Parameterized by Metric Spaces," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1737-1754, September.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:3:d:10.1007_s10959-019-00912-1
    DOI: 10.1007/s10959-019-00912-1
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    References listed on IDEAS

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    1. Lei, Pedro & Nualart, David, 2009. "A decomposition of the bifractional Brownian motion and some applications," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 619-624, March.
    2. Alexandre Richard, 2017. "Some Singular Sample Path Properties of a Multiparameter Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 30(4), pages 1285-1309, December.
    3. Lan, Xiaohong & Xiao, Yimin, 2018. "Strong local nondeterminism of spherical fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 44-50.
    4. Richard, Alexandre, 2015. "A fractional Brownian field indexed by L2 and a varying Hurst parameter," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1394-1425.
    5. Frédéric Lavancier, 2007. "Invariance principles for non-isotropic long memory random fields," Statistical Inference for Stochastic Processes, Springer, vol. 10(3), pages 255-282, October.
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