  The analytical techniques of the Nekhoroshev theorem are used to provide
estimates on the coefficient of Arnold diffusion along a particular resonance
in the Hamiltonian model of Froeschl\'{e} et al. (2000). A resonant normal form
is constructed by a computer program and the size of its remainder
$||R_{opt}||$ at the optimal order of normalization is calculated as a function
of the small parameter $\epsilon$. We find that the diffusion coefficient
scales as $D\propto||R_{opt}||^3$, while the size of the optimal remainder
scales as $||R_{opt}|| \propto\exp(1/\epsilon^{0.21})$ in the range
$10^{-4}\leq\epsilon \leq 10^{-2}$. A comparison is made with the numerical
results of Lega et al. (2003) in the same model.
