The symmetric binomial random walk is a canonical derivation of Brownian motion, $$dX_t = dB_t$$
Is there some way to derive a diffusion process from an asymmetric random walk? It seems like the asymmetry would work its way into the drift term $a$ in the diffusion, $$dX_t = at + bdB_t$$
But at the same time the Brownian motion term itself, in the canonical derivation, comes from the $1/2$ probability of the random walker moving left and right. So some of the asymmetrical motion should also contribute to the $dB_t$ term.