Control Problem on Space of Random Variables and Master Equation

Understand

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.