Abstract
Let u = {u(t,x),t ∈ [0,T],x ∈ ℝ} be a solution to a stochastic heat equation driven by a space-time white noise. We study that the realized power variation of the process u with respect to the time, properly normalized, has Gaussian asymptotic distributions. In particular, we study the realized power variation of the process u with respect to the time converges weakly to Brownian motion.
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The author wishes to express their deep gratitude to a referee for his/her valuable comments on an earlier version which improve the quality of this paper.
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Supported by ZJNSF (Grant No. LY20A010020) and NSFC (Grant No. 11671115)
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Wang, W.S. Asymptotic Distributions for Power Variation of the Solution to a Stochastic Heat Equation. Acta. Math. Sin.-English Ser. 37, 1367–1383 (2021). https://doi.org/10.1007/s10114-021-0267-z
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DOI: https://doi.org/10.1007/s10114-021-0267-z