Convergence rates in expectation for a nonlinear backward parabolic equation with Gaussian white noise
Analysis of PDEs
2017-11-30 v2 Mathematical Physics
math.MP
Probability
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.
Keywords
Cite
@article{arxiv.1711.10081,
title = {Convergence rates in expectation for a nonlinear backward parabolic equation with Gaussian white noise},
author = {Erkan Nane and Nguyen Huy Tuan},
journal= {arXiv preprint arXiv:1711.10081},
year = {2017}
}
Comments
29 pages, Submitted for publication