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.


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
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