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Regularity properties of the solution to a stochastic heat equation driven by a bifractional Brownian motion on S2

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  • Wang, Qingbo
  • Chen, Zhenlong

Abstract

This paper investigates the linear stochastic heat equation on the unit sphere S2 driven by an infinite dimensional bifractional Brownian noise. We prove the existence and uniqueness of the solution and establish the regularity properties of its sample path. Specifically, we examine the properties of strong local nondeterminism and derive the exact uniform modulus for the solution.

Suggested Citation

  • Wang, Qingbo & Chen, Zhenlong, 2025. "Regularity properties of the solution to a stochastic heat equation driven by a bifractional Brownian motion on S2," Statistics & Probability Letters, Elsevier, vol. 226(C).
    • Handle: RePEc:eee:stapro:v:226:y:2025:i:c:s0167715225001452
    DOI: 10.1016/j.spl.2025.110500
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    References listed on IDEAS

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    1. Nualart, Eulalia & Viens, Frederi, 2009. "The fractional stochastic heat equation on the circle: Time regularity and potential theory," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1505-1540, May.
    2. Tianshi Lu & Chunsheng Ma & Yimin Xiao, 2023. "Strong Local Nondeterminism and Exact Modulus of Continuity for Isotropic Gaussian Random Fields on Compact Two-Point Homogeneous Spaces," Journal of Theoretical Probability, Springer, vol. 36(4), pages 2403-2425, December.
    3. Lan, Xiaohong & Marinucci, Domenico & Xiao, Yimin, 2018. "Strong local nondeterminism and exact modulus of continuity for spherical Gaussian fields," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1294-1315.
    4. Russo, Francesco & Tudor, Ciprian A., 2006. "On bifractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 830-856, May.
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