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 $\log P_t(x, y)$.
Ann. Probab.
19(2):
538-561
(April, 1991).
DOI: 10.1214/aop/1176990440