On recovering parabolic diffusions from their time-averages
Analysis of PDEs
2020-01-14 v5
Abstract
The paper study a possibility to recover a parabolic diffusion from its time-average when the values at the initial time are unknown. This problem can be reformulated as a new boundary value problem where a Cauchy condition is replaced by a prescribed time-average of the solution. It is shown that this new problem is well-posed in certain classes of solutions. The paper establishes existence, uniqueness, and a regularity of the solution for this new problem and its modifications, including problems with singled out terminal values.
Cite
@article{arxiv.1609.01890,
title = {On recovering parabolic diffusions from their time-averages},
author = {Nikolai Dokuchaev},
journal= {arXiv preprint arXiv:1609.01890},
year = {2020}
}