No CrossRef data available.
Article contents
SOME FELLER SEMIGROUPS ON 
$C_{\infty }(\mathbb{R}^{n}\times \mathbb{Z}^{m})$ GENERATED BY PSEUDO-DIFFERENTIAL OPERATORS
Part of:
Miscellaneous topics - Partial differential equations
Markov processes
Groups and semigroups of linear operators, their generalizations and applications
Published online by Cambridge University Press: 15 April 2015
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.
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 
$\mathbb{R}^{n}\times \mathbb{R}^{n}\times \mathbb{Z}^{m}\times \mathbb{T}^{m}$.
Information
- Type
- Research Article
- Information
- Copyright
- Copyright © University College London 2015
References
Berg, Chr. and Forst, G., Potential Theory on Locally Compact Abelian Groups (Ergebnisse der Mathematik und ihrer Grenzgebiete (Ser. II) 87), Springer (Berlin, 1975).CrossRefGoogle Scholar
Böttcher, B., Schilling, R. and Wang, J., Lévy Type Processes: Construction, Approximation and Sample Path Properties (Lecture Notes in Mathematics 2099), Springer (Cham, 2013).Google Scholar
Courrège, Ph., Sur la forme intégro-différentielle des opérateurs de 
$C_{K}^{\infty }$ dans $C$ satisfaisant au principe du maximum. In: Sém. Théorie du Potentiel 1965/66. Exposé 2, 38pp.Google Scholar
$C_{K}^{\infty }$ dans 
$C$ satisfaisant au principe du maximum. In: Sém. Théorie du Potentiel 1965/66. Exposé 2, 38pp.Google ScholarEthier, S. N. and Kurtz, Th. G., Markov Processes – Characterization and Convergence (Wiley Series in Probability and Mathematical Statistics), Wiley (New York, 1986).CrossRefGoogle Scholar
Evans, K. and Jacob, N., Q-matrices as pseudo-differential operators with negative definite symbols. Math. Nachr. 286 2013, 631–640.CrossRefGoogle Scholar
Evans, K., Jacob, N. and Morris, O., On a class of pseudo-differential operators on ℝn ×ℤm generating Feller semigroups. Rev. Roumaine Math. Pures Appl. 59 2014, 55–75.Google Scholar
Jacob, N., A class of Feller semigroups generated by pseudo-differential operators. Math. Z. 215 1994, 151–166.CrossRefGoogle Scholar
Jacob, N., Pseudo-differential Operators and Markov Processes I. Fourier Analysis and Semigroups, Imperial College Press (London, 2001).Google Scholar
Jacob, N., Pseudo-differential Operators and Markov Processes II. Generators and their Potential Theory, Imperial College Press (London, 2002).CrossRefGoogle Scholar
Jacob, N., Knopova, V., Landwehr, S. and Schilling, R. L., A geometric interpretation of the transition density of a symmetric Lévy process. Sci. China Math. 55 2012, 1099–1126.CrossRefGoogle Scholar
Mao, X. and Yuan, C., Stochastic Differential Equations with Markov Switching, Imperial College Press (London, 2006).CrossRefGoogle Scholar
Maz’ya, V., Sobolev Spaces with Applications to Elliptic Partial Differential Equations, 2nd edn, revised and augmented (Grundlchren der mathematischen Wissenschaften 342), Springer (Berlin, 2011).CrossRefGoogle Scholar
Morris, O. C., On a class of one-parameter operator semigroups with state space $\mathbb{R}^{n}\times \mathbb{Z}^{m}$ generated by pseudo-differential operators. PhD Thesis, Swansea University, 2013.Google Scholar
$\mathbb{R}^{n}\times \mathbb{Z}^{m}$ generated by pseudo-differential operators. PhD Thesis, Swansea University, 2013.Google ScholarShen, C., PhD Thesis, Swansea University (in preparation).Google Scholar
You have
Access
- 2
- Cited by