On recovering parabolic diffusions from their time-averages

Nikolai Dokuchaev

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arXiv · 1609.01890

On recovering parabolic diffusions from their time-averages

Nikolai Dokuchaev

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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.

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Nikolai Dokuchaev. 2016-09-07. On recovering parabolic diffusions from their time-averages. https://arxiv.org/abs/1609.01890

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