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Stochastic wave equation with additive fractional noise: Solvability and global Hölder continuity

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  • Liu, Shuhui
  • Hu, Yaozhong
  • Wang, Xiong

Abstract

We determine the range of Hurst parameters that provide the necessary and sufficient conditions for the solvability, in L2(Ω), of the stochastic wave equation: ∂2∂t2u(t,x)=Δu(t,x)+W˙(t,x), where {W(t,x),t≥0,x∈Rd} is a fractional Brownian field with temporal Hurst parameter H0∈[12,1] and spatial Hurst parameters Hi ∈ (0, 1) for i=1,⋯,d. In particular, the solvability condition exhibits a phase transition at H0=1. We also obtain the sharp growth rate and the sharp Hölder continuity of the solution on the real line in the case H0=1/2.

Suggested Citation

  • Liu, Shuhui & Hu, Yaozhong & Wang, Xiong, 2026. "Stochastic wave equation with additive fractional noise: Solvability and global Hölder continuity," Stochastic Processes and their Applications, Elsevier, vol. 198(C).
    • Handle: RePEc:eee:spapps:v:198:y:2026:i:c:s0304414926000967
    DOI: 10.1016/j.spa.2026.104964
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