In this paper we study the transition density $P_t(x, y)$ of a nondegenerate diffusion process by using the stochastic control method invented by Fleming and the idea of stochastic parallel translation. We obtain a two-sided estimate for $P_t(x, y)$ as well as some bounds for the derivatives of $\log P_t(x, y)$.
Shuenn-Jyi Sheu. "Some Estimates of the Transition Density of a Nondegenerate Diffusion Markov Process." Ann. Probab. 19 (2) 538 - 561, April, 1991. https://doi.org/10.1214/aop/1176990440