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Estimates for the Derivative of Diffusion Semigroups

   
@article{ECP994,
	author = {L. Rincon},
	title = {Estimates for the Derivative of Diffusion Semigroups},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {3},
	year = {1998},
	keywords = {Diffusion Semigroups, Diffusion Processes, Stochastic Differential Equations.},
	abstract = {Let $\{P_t\}_{t\ge 0}$ 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 Frechet derivative of the semigroups associated with the operators ${\cal A}+V$ and ${\cal A}+Z\cdot\nabla$ where ${\cal A}$ is the generator of a diffusion process, $V$ is a potential and $Z$ is a vector field.},
	pages = {no. 8, 65-74},
	issn = {1083-589X},
	doi = {10.1214/ECP.v3-994},    
        url = {http://ecp.ejpecp.org/article/view/994}}