## Electronic Communications in Probability

### Estimates for the Derivative of Diffusion Semigroups

L. Rincon

#### 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.

#### Article information

Source
Electron. Commun. Probab., Volume 3 (1998), paper no. 8, 65-74.

Dates
Accepted: 18 August 1998
First available in Project Euclid: 2 March 2016

https://projecteuclid.org/euclid.ecp/1456935914

Digital Object Identifier
doi:10.1214/ECP.v3-994

Mathematical Reviews number (MathSciNet)
MR1641074

Zentralblatt MATH identifier
0920.47040

Rights

#### Citation

Rincon, L. Estimates for the Derivative of Diffusion Semigroups. Electron. Commun. Probab. 3 (1998), paper no. 8, 65--74. doi:10.1214/ECP.v3-994. https://projecteuclid.org/euclid.ecp/1456935914

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