On the binomial approximation of the American put

We consider the binomial approximation of the American put price in the Black-Scholes model (with continuous dividend yield). Our main result is that the error of approximation is $O((lnn)$\alpha$\mathrm{/}n)$ where n is the number of time periods and the exponent $\alpha$ is a positive number, the value of which may differ according to the respective levels of the interest rate and the dividend yield.