Abstract
Consider the stochastic partial differential equation
du ∈(t,x) = θ(t)△u ∈(t, x)dt + ∈dW Q(t,x), 0 ≤ t ≤ T
where △ = ∂2/∂x 2, θ ∈ Θ and Θ is a class of positive valued functions. We obtain an estimator for the linear multiplier θ (t) and establish the consistency, rate of convergence and asymptotic normality of this estimator as θ → 0.
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Rao, B.L.S.P. Nonparametric Inference for a Class of Stochastic Partial Differential Equations II. Statistical Inference for Stochastic Processes 4, 41–52 (2001). https://doi.org/10.1023/A:1017524901430
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DOI: https://doi.org/10.1023/A:1017524901430