
Nonparametric calibration for stochastic reactiondiffusion equations based on discrete observations
Nonparametric estimation for semilinear SPDEs, namely stochastic reactio...
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Parametric estimation for a parabolic linear SPDE model based on sampled data
We consider parametric estimation for a parabolic linear second order st...
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Nonparametric estimation for linear SPDEs from local measurements
We estimate the coefficient function of the leading differential operato...
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Parameter estimation for discretely sampled stochastic heat equation driven by spaceonly noise revised
The main goal of this paper is to build consistent and asymptotically no...
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Adaptive estimator for a parabolic linear SPDE with a small noise
We deal with parametric estimation for a parabolic linear second order s...
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Nonlinear reduced models for state and parameter estimation
State estimation aims at approximately reconstructing the solution u to ...
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QKD parameter estimation by twouniversal hashing leads to faster convergence to the asymptotic rate
This paper proposes and proves security of a QKD protocol which uses two...
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Parameter estimation for SPDEs based on discrete observations in time and space
Parameter estimation for a parabolic, linear, stochastic partial differential equation in one space dimension is studied observing the solution field on a discrete grid in a fixed bounded domain. Considering an infill asymptotic regime in both coordinates, we prove central limit theorems for realized quadratic variations based on temporal and spatial increments as well as on double increments in time and space. Resulting method of moments estimators for the diffusivity and the volatility parameter inherit the asymptotic normality and can be constructed robustly with respect to the sampling frequencies in time and space. Upper and lower bounds reveal that the optimal convergence rate for joint estimation of the parameters is slower than the usual parametric rate in general. The theoretical results are illustrated in a numerical example.
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