On The Interpretation Of The Master Equation
Abstract
Since its introduction by P.L. Lions in his lectures and seminars at the College de France, see [9], and also the very helpful notes of Cardialaguet [4] on Lions' lectures, the Master Equation has attracted a lot of interest, and various points of view have been expressed, see for example Carmona-Delarue [5], Bensoussan-Frehse-Yam [2], Buckdahn-Li-Peng-Rainer [3]. There are several ways to introduce this type of equation; and in those mentioned works, they involve an argument which is a probability measure, while P.L. Lions has recently proposed the idea of working with the Hilbert space of square integrable random variables. Hence writing the equation is an issue; while another issue is its origin. In this article, we discuss all these various aspects, and our modeling argument relies heavily on a seminar at College de France delivered by P.L. Lions on November 14, 2014.
Cite
@article{arxiv.1503.07754,
title = {On The Interpretation Of The Master Equation},
author = {Alain Bensoussan and Jens Frehse and Phillip Yam},
journal= {arXiv preprint arXiv:1503.07754},
year = {2015}
}