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1998 Estimates for the Derivative of Diffusion Semigroups
L. Rincon
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Electron. Commun. Probab. 3: 65-74 (1998). DOI: 10.1214/ECP.v3-994

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.

Citation

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L. Rincon. "Estimates for the Derivative of Diffusion Semigroups." Electron. Commun. Probab. 3 65 - 74, 1998. https://doi.org/10.1214/ECP.v3-994

Information

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

zbMATH: 0920.47040
MathSciNet: MR1641074
Digital Object Identifier: 10.1214/ECP.v3-994

Subjects:
Primary: 47D07
Secondary: 60H10, 60J55

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