×

Estimates for the derivative of diffusion semigroups. (English) Zbl 0920.47040

Summary: Let \(\{P_t\}_{t\geq 0}\) be the transition semigroup of a diffusion process. It is known that \(P_t\) sends continuous functions into differentiable functions so we can write \(DP_tf\). But what happens with this derivative when \(t\to 0\) and \(P_0f=f\) is only continuous? We give estimates for the supremum norm of the Fréchet derivative of the semigroups associated with the operators \({\mathcal A}+V\) and \({\mathcal A}+Z\cdot\nabla\) where \({\mathcal A}\) is the generator of a diffusion process, \(V\) is a potential and \(Z\) is a vector field.

MSC:

47D07 Markov semigroups and applications to diffusion processes
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J55 Local time and additive functionals
PDFBibTeX XMLCite
Full Text: DOI EuDML EMIS