An extended generator and Schrödinger equations

Electronic Journal of Probability

Volumn 4, Issue , 1999, Pages 1-23

  Getoor, R K ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Generators; Markov processes; Schr dinger equations; Smooth measures

Indexed keywords

EID: 0003322648     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v4-56     Document Type: Article

References (21)

1. S. Albeverio, J. Brasche and M. Rockner, Dirichlet forms and generalized Schrodinger operators, Lecture Notes in Physics 345, Springer, 1989, pp. 1-42
2. J. Azema, Théorie générale des processus et retournement du temps, Ann. Sci. de l’Ecole Norm. Sup. 6 (1973), 459-519.
3. R. M. Blumenthal and R. K. Getoor, Markov Processes and Potential Theory, Academic Press, New York, 1968.
4. A. Boukricha, W. Hansen and H. Hueber, Continuous solutions of the generalized Schrodinger equation and perturbation of harmonic spaces, Expo. Math. 5 (1987), 97-135.
5. K. L. Chung and Z. Zhao, From Brownian Motion to Schrodinger’s Equation, Springer, Berlin, Heidelberg, New York, 1995.
6. E. Cinlar, J. Jacod, P. Protter and M. J. Sharpe, Semimartingales and Markov processes, Z. Wahrsheinlichkeitstheorie 54, (1980), 161-219.
7. C. Dellacherie et P. A. Meyer, Probabilites et Potentiel, Ch. I-IV (1975), Ch. V-VIII (1980), Ch. IX-XI (1983), Ch. XII-XVI (1987) Hermann, Paris.
8. E. B. Dynkin, Markov Processes, vol. 1, Springer, Berlin, Heidelberg, New York, 1965.
9. D. Feyel and A. de La Pradelle, Etude de l’équation 1/2Δu – uμ = 0 ou μ est une mesure positive, Ann. Inst. Fourier, Grenoble 38 (1988), 199-218.
10. P. J. Fitzsimmons and R. K. Getoor, Revuz measures and time changes, Math. Z. 199 (1988), 233-256.
11. P. J. Fitzsimmons and R. K. Getoor,, Smooth measures and continuous additive functionals of right Markov processes, Ito’s Stochastic Calculus and Probability Theory, Springer, Berlin, Heidelberg, New York, 1996, pp. 31-49.
12. R. K. Getoor, Excessive Measures, Birkhauser, Boston, 1990.
13. R. K. Getoor, Measure perturbations of Markovian semigroups, Potential Analysis 11 (1999), 101-133.
14. R. K. Getoor and M. J. Sharpe, Naturality, standardness and weak duality, Z. Wahrsheinlichkeitstheorie verw. Geb. 67 (1984), 1-62.
15. R. K. Getoor and J. Steffens, The energy functional, balayage and capacity, Ann. Inst. Henri Poincare 23 (1987), 321-357.
16. W. Hansen, A note on continuous solutions of the Schrodinger equation, Proc. AMS 117 (1993), 381-384.
17. H. Kunita, Absolute continuity of Markov processes and generators, Nagoya Math. J. 36 (1969), 1-26.
18. Z. Ma, Some new results concerning Dirichlet forms, Feynman-Kac semigroups and Schrodinger equations, Contemporary Math. 118 (1991), 239-254.
19. D. Revuz, Mesures associées aux fonctionnelles additive de Markov I, Trans. AMS 148 (1970), 501-531.
20. M. J. Sharpe, General Theory of Markov Processes, Academic Press, Boston, San Diego, New York, 1988.
21. P. Stollmann and J. Voigt, Perturbations of Dirichlet forms by measures, Potential Analysis 5 (1996), 109-139.