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A multiparameter Garsia–Rodemich–Rumsey inequality and some applications

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  • Hu, Yaozhong
  • Le, Khoa

Abstract

We extend the classical Garsia–Rodemich–Rumsey inequality to the multiparameter situation. The new inequality is applied to obtain some joint Hölder continuity along the rectangles for fractional Brownian fields W(t,x) and for the solution u(t,y) of the stochastic heat equation with additive white noise.

Suggested Citation

  • Hu, Yaozhong & Le, Khoa, 2013. "A multiparameter Garsia–Rodemich–Rumsey inequality and some applications," Stochastic Processes and their Applications, Elsevier, vol. 123(9), pages 3359-3377.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:9:p:3359-3377
    DOI: 10.1016/j.spa.2013.04.019
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    Cited by:

    1. Nummi, Patrik & Viitasaari, Lauri, 2024. "Necessary and sufficient conditions for continuity of hypercontractive processes and fields," Statistics & Probability Letters, Elsevier, vol. 208(C).
    2. Hu, Yaozhong & Lê, Khoa & Mytnik, Leonid, 2017. "Stochastic differential equation for Brox diffusion," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2281-2315.

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