  Consider a non-symmetric generalized diffusion $X(\cdot)$ in ${\bbR}^d$
determined by the differential operator $A(\msx)=-\sum_{ij}
\partial_ia_{ij}(\msx)\partial_j +\sum_i b_i(\msx)\partial_i$. In this paper
the diffusion process is approximated by Markov jump processes $X_n(\cdot)$, in
homogeneous and isotropic grids $G_n \subset {\bbR}^d$, which converge in
distribution to the diffusion $X(\cdot)$. The generators of $X_n(\cdot)$ are
constructed explicitly. Due to the homogeneity and isotropy of grids, the
proposed method for $d\geq3$ can be applied to processes for which the
diffusion tensor $\{a_{ij}(\msx)\}_{11}^{dd}$ fulfills an additional condition.
The proposed construction offers a simple method for simulation of sample paths
of non-symmetric generalized diffusion. Simulations are carried out in terms of
jump processes $X_n(\cdot)$. For $d=2$ the construction can be easily
implemented into a computer code.
