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SOME FELLER SEMIGROUPS ON $C_{\infty }(\mathbb{R}^{n}\times \mathbb{Z}^{m})$ GENERATED BY PSEUDO-DIFFERENTIAL OPERATORS

Part of: Groups and semigroups of linear operators, their generalizations and applications Miscellaneous topics - Partial differential equations Markov processes

Published online by Cambridge University Press:  15 April 2015

Kristian P. Evans ,
Niels Jacob  and
Chenglin Shen
Kristian P. Evans
Affiliation:
Mathematics Department, Swansea University, Singleton Park, Swansea SA2 8PP, U.K. email K.Evans@Swansea.ac.uk
Niels Jacob
Affiliation:
Mathematics Department, Swansea University, Singleton Park, Swansea SA2 8PP, U.K. email N.Jacob@Swansea.ac.uk
Chenglin Shen
Affiliation:
Mathematics Department, Swansea University, Singleton Park, Swansea SA2 8PP, U.K. email 570124@Swansea.ac.uk
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Abstract

In this paper we construct some Feller semigroups, hence Feller processes, with state space $\mathbb{R}^{n}\times \mathbb{Z}^{m}$ starting with pseudo-differential operators having symbols defined on $\mathbb{R}^{n}\times \mathbb{R}^{n}\times \mathbb{Z}^{m}\times \mathbb{T}^{m}$.

MSC classification

Primary: 35S99: None of the above, but in this section 47D07: Markov semigroups and applications to diffusion processes 60J35: Transition functions, generators and resolvents
Type
Research Article
Information
Mathematika , Volume 61 , Issue 2 , May 2015 , pp. 402 - 413
Copyright
Copyright © University College London 2015 

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