On the domain of a Fleming--Viot-type operator on an  -space with invariant measure

doi:10.1285/i15900932v31n1p139

On the domain of a Fleming--Viot-type operator on an $L^p$ -space with invariant measure

Delio Mugnolo, Abdelaziz Rhandi

Abstract

We characterize the domain of a Fleming-Viot type operator of the form $L\varphi(x)$ := $\sum_{i=1}^Nx_i(1-x_i)D_{ii}\varphi(x)+\sum_{i=1}^N(\alpha_i(1-x_i)-\alpha_{i+1}x_i)D_i\varphi(x)$ on $L^p([0,1]^N,\mu)$ for $1<p<\infty$ , where $\mu$ is the corresponding invariant measure. Our approach relies on the characterization of the domain of the one-dimensional Fleming-Viot operator and the Dore-Venni operator sum method.

DOI Code: 10.1285/i15900932v31n1p139

Keywords: Fleming--Viot process; degenerate elliptic problems; analytic $C_0$-semigroups

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On the domain of a Fleming--Viot-type operator on an -space with invariant measure

Abstract

On the domain of a Fleming--Viot-type operator on an $L^p$ -space with invariant measure