Nonparametric velocity estimation in stochastic convection-diffusion equations from multiple local measurements

TY - UNPB

T1 - Nonparametric velocity estimation in stochastic convection-diffusion equations from multiple local measurements

AU - Strauch, Claudia

AU - Tiepner, Anton

N1 - 37 pages, 1 figure

PY - 2024/2/13

Y1 - 2024/2/13

N2 - We investigate pointwise estimation of the function-valued velocity field of a second-order linear SPDE. Based on multiple spatially localised measurements, we construct a weighted augmented MLE and study its convergence properties as the spatial resolution of the observations tends to zero and the number of measurements increases. By imposing Hölder smoothness conditions, we recover the pointwise convergence rate known to be minimax-optimal in the linear regression framework. The optimality of the rate in the current setting is verified by adapting the lower bound ansatz based on the RKHS of local measurements to the nonparametric situation.

AB - We investigate pointwise estimation of the function-valued velocity field of a second-order linear SPDE. Based on multiple spatially localised measurements, we construct a weighted augmented MLE and study its convergence properties as the spatial resolution of the observations tends to zero and the number of measurements increases. By imposing Hölder smoothness conditions, we recover the pointwise convergence rate known to be minimax-optimal in the linear regression framework. The optimality of the rate in the current setting is verified by adapting the lower bound ansatz based on the RKHS of local measurements to the nonparametric situation.

U2 - 10.48550/arXiv.2402.08353

DO - 10.48550/arXiv.2402.08353

M3 - Preprint

BT - Nonparametric velocity estimation in stochastic convection-diffusion equations from multiple local measurements

ER -