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Maximal moments and uniform modulus of continuity for stable random fields

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  • Panigrahi, Snigdha
  • Roy, Parthanil
  • Xiao, Yimin

Abstract

In this work, we provide sharp bounds on the rate of growth of maximal moments for stationary symmetric stable random fields when the underlying nonsingular group action (or its restriction to a suitable lower rank subgroup) has a nontrivial dissipative component. We also investigate the relationship between this rate of growth and the path regularity properties of self-similar stable random fields with stationary increments, and establish uniform modulus of continuity of such fields. In the process, a new notion of weak effective dimension is introduced for stable random fields and is connected to maximal moments and path properties.

Suggested Citation

  • Panigrahi, Snigdha & Roy, Parthanil & Xiao, Yimin, 2021. "Maximal moments and uniform modulus of continuity for stable random fields," Stochastic Processes and their Applications, Elsevier, vol. 136(C), pages 92-124.
  • Handle: RePEc:eee:spapps:v:136:y:2021:i:c:p:92-124
    DOI: 10.1016/j.spa.2021.02.002
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    References listed on IDEAS

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    1. Fasen, Vicky & Roy, Parthanil, 2016. "Stable random fields, point processes and large deviations," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 832-856.
    2. Ayache, Antoine & Roueff, François & Xiao, Yimin, 2009. "Linear fractional stable sheets: Wavelet expansion and sample path properties," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1168-1197, April.
    3. Biermé, Hermine & Lacaux, Céline, 2009. "Hölder regularity for operator scaling stable random fields," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2222-2248, July.
    4. Resnick, Sidney & Samorodnitsky, Gennady, 2004. "Point processes associated with stationary stable processes," Stochastic Processes and their Applications, Elsevier, vol. 114(2), pages 191-209, December.
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