We study so called Varadhan type short time asymptotic estimates of heat kernels and Shilder type large deviation for Brownian motion on some affme nested fractals introduced in [7]. As a corollary to our approach, we obtain sharper estimates of heat kernels for a class of one dimensional diffusion processes studied in [8].
Takashi Kumagai, Short Time Asymptotic Behaviour and Large Deviation for Brownian Motion on Some Affine Nested Fractals. Publ. Res. Inst. Math. Sci. 33 (1997), no. 2, pp. 223–240
DOI 10.2977/PRIMS/1195145448