## Some estimates of the transition density of a nondegenerate diffusion Markov process.(English)Zbl 0738.60060

It is considered the difficult problem of estimating the transition density $$P_ t(x,y)$$ for a nondegenerate diffusion process using Fleming’s logarithmic transformation and the corresponding nonlinear dynamic programming equation of a stochastic control problem. Estimate of $$D^ m_ x \log P_ t(x,y)$$ instead of $$D^ m_ xP_ t(x,y)$$ brings difficulties which are avoided using a stochastic parallel translation. Two theorems and seven lemmas are proved.

### MSC:

 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60J35 Transition functions, generators and resolvents 60J60 Diffusion processes 60H07 Stochastic calculus of variations and the Malliavin calculus
Full Text: