This paper studies an asymptotic solvability problem for linear quadratic (LQ) mean field games with controlled diffusions and indefinite weights the state control in costs. The authors employ a rescaling approach to derive low dimensional Riccati ordinary differential equation (ODE) system, which characterizes necessary sufficient condition solvability. technique is further used performance es...

This paper is concerned with two-person mean-field linear-quadratic non-zero sum stochastic differential games in an infinite horizon. Both open-loop and closed-loop Nash equilibria are introduced. The existence of equilibrium characterized by the solvability a system forward-backward equations horizon convexity cost functionals, representation given through solution to two coupled non-symmetri...

Let k be a function field of one variable over a finite field with the characteristic not equal to two. In this paper, we consider the prehomogeneous representation of the space of binary quadratic forms over k. We have two main results. The first result is on the principal part of the global zeta function associated with the prehomogeneous vector space. The second result is on a mean value the...