Olena Kapustian, Nina Kasimova
abstract:
We study the problem of minimax estimation of functionals depending on the
solutions of parabolic boundary value problems, where the observation model is
based on time-averaging. Using the averaging method, we construct approximate
minimax estimates and analyze the corresponding estimation errors. The obtained
results show that the averaging approach provides effective tools for reducing
the complexity of minimax estimation in parabolic systems with rapidly
oscillating coefficients.
Mathematics Subject Classification: 35K20, 35B27, 93C20
Key words and phrases: Averaging method, observation, minimax estimation, parabolic problem