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The heat equation given a time series of initial data subject to error

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  • Hesse C. H.

Abstract

The Cauchy problem for the one-dimensional heat equation asks for solutions uf(x,t) of ∂u/∂t = ∂2u / ∂x2 on R × [1, ∞) with u(x, 1) = f(x) on R. Here we assume that the initial condition f(x), x ∊ R, and hence the solution uf is unknown but that at times tj, j = 1, 2, …, n, noisy measurements are available from which an estimator ~fn of the initial condition may be obtained. The paper studies the asymptotics (as t → ∞ and n → ∞) of uf(xt1/2, t)–u~fn(xt1/2, t) in mean integrated squared error.

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  • Hesse C. H., 2005. "The heat equation given a time series of initial data subject to error," Statistics & Risk Modeling, De Gruyter, vol. 23(4/2005), pages 317-329, April.
    • Handle: RePEc:bpj:strimo:v:23:y:2005:i:4/2005:p:317-329:n:4
    DOI: 10.1524/stnd.2005.23.4.317
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    References listed on IDEAS

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    1. Stefanski, Leonard A., 1990. "Rates of convergence of some estimators in a class of deconvolution problems," Statistics & Probability Letters, Elsevier, vol. 9(3), pages 229-235, March.
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