Long-term returns in stochastic interest rate models

In this paper, we observed the convergence of the long-term return, using an extension of the Cox-Ingersoll-Ross (1985) stochastic model of the short interest rate r. Using the theory of Bessel processes, we were able to prove the convergence almost everywhere of (1/t)f0tXs ds with X a generalized Bessel-square process with drift to a stochastic reversion level.