Construction of time-inhomogeneous Markov processes via evolution equations using pseudo-differential operators

Journal of the London Mathematical Society

Volumn 78, Issue 3, 2008, Pages 605-621

  Böttcher, Björn ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 56449097541     PISSN: 00246107     EISSN: 14697750     Source Type: Journal    
DOI: 10.1112/jlms/jdn043     Document Type: Article

References (12)

1. C. BERG and G. FORST, Potential theory on locally compact abelian groups, Ergebnisse der Mathematik und ihrer Grenzgebiete 87 (Springer, Berlin, 1975).
2. B. BÖTTCHER, 'Some investigations on Feller processes generated by pseudo-differential operators', PhD Thesis, University of Wales, Swansea, 2004.
3. B. BÖTTCHER, 'A parametrix construction for the fundamental solution of the evolution equation associated with a pseudo-differential operator generating a Markov process', Math. Nachr. 278 (2005) 1235-1241.
4. ∞ dans C satisfaisant au principe du maximum', Sémi, Théorie du potentiel, Exposé 2, 1965/66, 38pp.
5. S. EIDELMAN, S. IVASYSHEN and A. KOCHUBEI, Analytic methods in the theory of differential and pseudo-differential equations of parabolic type, Operator Theory, Advances and Applications 152 (Birkhäuser, Basel, 2004).
6. W. HOH, 'A symbolic calculus for pseudo differential operators generating Feller semigroups', Osaka Math. J. 35 (1998) 789-820.
7. W. HOH, Pseudo differential operators generating Markov processes, Habilitationsschrift, Universität Bielefeld, Bielefeld, 1998.
8. N. JACOB, Pseudo-differential operators and Markov processes I. Fourier analysis and semigroups (Imperial College Press, London, 2001).
9. N. JACOB, Pseudo-differential operators and Markov processes II. Generators and their potential theory (Imperial College Press, London, 2002).
10. N. JACOB, Pseudo-differential operators and Markov processes III. Markov processes and applications (Imperial College Press, London, 2005).
11. H. KUMANO-GO, Pseudo-differential operators (MIT Press, Cambridge, MA, 1974).
12. C. TSUTSUMI, 'The fundamental solution for a degenerate parabolic pseudo-differential operator', Proc. Japan Acad. 50 (1974) 11-15.