It is shown in this paper that the transition kernel corresponding to a spatially inhomogeneous random walk on Zd admits upper and lower Gaussian estimates.
@article{1140191538,
author = {Mustapha, Sami},
title = {Gaussian estimates for spatially inhomogeneous random walks on Z<sup>
d
</sup>},
journal = {Ann. Probab.},
volume = {34},
number = {1},
year = {2006},
pages = { 264-283},
language = {en},
url = {http://dml.mathdoc.fr/item/1140191538}
}
Mustapha, Sami. Gaussian estimates for spatially inhomogeneous random walks on Z
d
. Ann. Probab., Tome 34 (2006) no. 1, pp. 264-283. http://gdmltest.u-ga.fr/item/1140191538/