ON THE FUNDAMENTAL SOLUTION AND A VARIATIONAL FORMULATION FOR A DEGENERATE DIFFUSION OF KOLMOGOROV TYPE.

Duong, Manh Hong; Tran, Hoang Minh

In this paper, we construct the fundamental solution to a degenerate diffusion of Kolmogorov type and develop a time-discrete variational scheme for its adjoint equation. The so-called mean squared derivative cost function plays a crucial role occurring in both the fundamental solution and the variational scheme. The latter is implemented by minimizing a free energy functional with respect to the Kantorovich optimal transport cost functional associated with the mean squared derivative cost. We establish the convergence of the scheme to the solution of the adjoint equation generalizing previously known results for the Fokker-Planck equation and the Kramers equation.

DIFFERENTIAL equations; ORDINARY differential equations; NUMERICAL analysis; ESTIMATION theory

Discrete & Continuous Dynamical Systems: Series A, 2018, Vol 38, Issue 7, p3407

1078-0947

Academic Journal

10.3934/dcds.2018146