  We consider a multidimensional Markov Chain $X$ converging to a
multidimensional Brownian Motion. We construct a positive harmonic function for
$X$ killed on exiting the cone. We show that its asymptotic behavior is similar
to that of to the harmonic function of Brownian motion. We use the harmonic
function to study the asymptotic behaviour of the tail distribution of the exit
time $\tau$ of $X$ from a cone.
