Convergence rates in expectation for a nonlinear backward parabolic equation with Gaussian white noise

Abstract

The main purpose of this paper is to study the problem of determining initial condition of nonlinear parabolic equation from noisy observations of the final condition. We introduce a regularized method to establish an approximate solution. We prove an upper bound on the rate of convergence of the mean integrated squared error.

arXiv comment29 pages, Submitted for publication

References in corpus (1)

• Characterizations of variational source conditions, converse results, and maxisets of spectral regularization methods