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The Second-Order Master Equation
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This chapter investigates the second-order master equation with common noise, which requires the well-posedness of the mean field game (MFG) system. It also defines and analyzes the solution of the master equation. The chapter explains the forward component of the MFG system that is recognized as the characteristics of the master equation. The regularity of the solution of the master equation is explored through the tangent process that solves the linearized MFG system. It also analyzes first-order differentiability and second-order differentiability in the direction of the measure on the same model as for the first-order derivatives. This chapter concludes with further description of the derivation of the master equation and well-posedness of the stochastic MFG system.
Title: The Second-Order Master Equation
Description:
This chapter investigates the second-order master equation with common noise, which requires the well-posedness of the mean field game (MFG) system.
It also defines and analyzes the solution of the master equation.
The chapter explains the forward component of the MFG system that is recognized as the characteristics of the master equation.
The regularity of the solution of the master equation is explored through the tangent process that solves the linearized MFG system.
It also analyzes first-order differentiability and second-order differentiability in the direction of the measure on the same model as for the first-order derivatives.
This chapter concludes with further description of the derivation of the master equation and well-posedness of the stochastic MFG system.
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