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Quasi-likelihood estimation for stochastic fractional heat equation

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  • Sun, Yaqin
  • Han, Jingqi
  • Yan, Litan

Abstract

By the quasi-likelihood method, in this note we consider parameter estimation of the fractional heat equation ∂∂tu(t,x)=Δαu(t,x)dt+σẆ(t,x),t≥0,x∈Rwith initial condition u(0,x)=0, where Ẇ(t,x) is a space–time white noise and Δα=−(−Δ)α/2 is the fractional Laplacian with α∈(1,2]. By using the quasi-likelihood method we obtain the estimator of σ2 and give the asymptotic behaviors of the estimator provided that the spatial process x↦u(t,x) can be observed at some discrete points {xj=jh,j=0,1,2,…,n} with h=h(n)→0, nh1+γ→R≠0 for some 0≤γ<1, as n→∞.

Suggested Citation

  • Sun, Yaqin & Han, Jingqi & Yan, Litan, 2026. "Quasi-likelihood estimation for stochastic fractional heat equation," Statistics & Probability Letters, Elsevier, vol. 227(C).
    • Handle: RePEc:eee:stapro:v:227:y:2026:i:c:s0167715225001944
    DOI: 10.1016/j.spl.2025.110549
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    References listed on IDEAS

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    1. Cialenco, Igor & Kim, Hyun-Jung, 2022. "Parameter estimation for discretely sampled stochastic heat equation driven by space-only noise," Stochastic Processes and their Applications, Elsevier, vol. 143(C), pages 1-30.
    2. Yaozhong Hu & David Nualart & Hongjuan Zhou, 2019. "Parameter estimation for fractional Ornstein–Uhlenbeck processes of general Hurst parameter," Statistical Inference for Stochastic Processes, Springer, vol. 22(1), pages 111-142, April.
    3. Debbi, Latifa & Dozzi, Marco, 2005. "On the solutions of nonlinear stochastic fractional partial differential equations in one spatial dimension," Stochastic Processes and their Applications, Elsevier, vol. 115(11), pages 1764-1781, November.
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