Log-Harnack Inequality and Exponential Ergodicity for Distribution Dependent CKLS and Vasicek Model

Abstract

In this paper, Wang's log-Harnack inequality and exponential ergodicity are derived for two types of distribution dependent SDEs: one is the CKLS model, where the diffusion coefficient is a power function of order θ with θ ∈ [ 1 2 , 1); the other one is Vasicek model, where the diffusion coefficient only depends on distribution. Both models in the distribution independent case are used to characterize the interest rate in finance.

Entropy Estimate Between Diffusion Processes and Application to McKean-Vlasov SDEs

“…However, if the noise coefficient is also distribution dependent, the coupling by change of measures applied in the above references does not apply. Recently, for σ(t, x, µ) = σ(t, µ) independent of the spatial variable x, (1.8) has been established in [11] by using a noise decomposition argument, see also [3] for the study on a special model.…”