Control problem on space of random variables and master equation
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Publication:5107913
DOI10.1051/COCV/2018034zbMATH Open1450.35305arXiv1508.00713OpenAlexW2963359377MaRDI QIDQ5107913
Author name not available (Why is that?)
Publication date: 29 April 2020
Published in: (Search for Journal in Brave)
Abstract: We study in this paper a control problem in a space of random variables. We show that its Hamilton Jacobi Bellman equation is related to the Master equation in Mean field theory. P.L. Lions in [14,15] introduced the Hilbert space of square integrable random variables as a natural space for writing the Master equation which appears in the mean field theory. W. Gangbo and A. 'Swik{e}ch [10] considered this type of equation in the space of probability measures equipped with the Wasserstein metric and use the concept of Wasserstein gradient. We compare the two approaches and provide some extension of the results of Gangbo and 'Swik{e}ch.
Full work available at URL: https://arxiv.org/abs/1508.00713
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