ISSN:
1432-2064
Keywords:
Mathematics Subject Classification (1991): 60G, 62G, 35R
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract For linear partial differential equations, some inverse source problems are treated statistically based on nonparametric estimation ideas. By observing the solution in a small Gaussian white noise, the kernel type of estimators is used to estimate the unknown source function and its partial derivatives.. It is proved that such estimators are consistent as the noise intensity tends to zero. Depending on the principal part of the differential operator, the optimal asymptotic rate of convergence is ascertained within a wide class of risk functions in a minimax sense.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s004400050212
Permalink