Geodesic
On the asymptotics of the transition probability density of processes with small diffusion
Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 3, pp. 527-536

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Let $x_s^{\varepsilon}$ be a diffusion process with the infinitesimal operator given by (3), and let $p^{\varepsilon}(t,x,y)$ be the transition probability density of $x_s^{\varepsilon}$. The aim of the article is to prove that the asymptotics of $p^{\varepsilon}(t,x,y)$ has the form of (4) if $t$ and the distance between $x$ and $y$ are sufficiently small. We calculate the principal term of the asymptotics and deduce recurrent formulas for the others. 
@article{TVP_1976_21_3_a4,
     author = {Yu. I. Kifer},
     title = {On the asymptotics of the transition probability density of processes with small diffusion},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {527--536},
     publisher = {mathdoc},
     volume = {21},
     number = {3},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1976_21_3_a4/}
}
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Yu. I. Kifer. On the asymptotics of the transition probability density of processes with small diffusion. Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 3, pp. 527-536. http://geodesic.mathdoc.fr/item/TVP_1976_21_3_a4/