Electronic Communications in Probability

Estimates for the Derivative of Diffusion Semigroups

L. Rincon

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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

Permanent link to this document
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

Subjects
Primary: 47D07: Markov semigroups and applications to diffusion processes {For Markov processes, see 60Jxx}
Secondary: 60J55: Local time and additive functionals 60H10: Stochastic ordinary differential equations [See also 34F05]

Keywords
Diffusion Semigroups Diffusion Processes Stochastic Differential Equations

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

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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