Capacity and energy for multiparameter Markov processes

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1. [A] J. Azéma, Une remarque sur les temps de retour. Trois applications, Séminaire de Probabilités VI; Lecture Notes in Mathematics, No. 258, pp. 35-50, Springer Verlag, Berlin-Heidelberg-New York, 1972. Zbl0231.60066MR381010
2. [B] D. Bakry, Théorèmes de section et de projection pour les processus à deux indices, Z. Wahrscheinlichkeitstheorie verw. Geb., Vol. 55, 1981, pp. 55-71. Zbl0431.60057MR606006
3. [BG] R.M. Blumenthal and R.K. Getoor, Markov Processes and Potential Theory, Academic Press, New York, 1968. Zbl0169.49204MR264757
4. [DM] C. Dellacherie and P.-A. Meyer, Probabilités et Potentiel, Ch. V-VII, Hermann, Paris, 1980. Zbl0464.60001MR488194
5. C. Dellacherie and P.-A. Meyer, Probabilités et Potentiel, Ch. XII-XVI, Hermann, Paris, 1987. MR488194
6. [D] E.B. Dynkin, Markov Systems and their Additive Functionals, Ann. Probab., Vol. 5, 1977, pp. 653-677. Zbl0379.60076MR451415
7. E.B. Dynkin, Additive Functionals of Several Time-Reversible Markov Processes, J. Funct. Anal., Vol. 42, 1981, pp. 64-101. Zbl0467.60069MR620580
8. [E] S.N. Evans, Multiple Points in the Sample Paths of a Lévy Process, Probab. Th. Rel. Fields, Vol. 76, 1987, pp. 359-367. MR912660
9. S.N. Evans, Potential Theory for a Family of Several Markov Processes, Ann. Inst. Henri Poincaré, Vol. 23, 1987, pp. 499-530. Zbl0625.60086MR906728
10. [Fi] P.J. Fitzsimmons, Homogeneous Random Measures and a Weak Order for the Excessive Measures of a Markov Process, Trans. Amer. Math. Soc., Vol. 303, 1987, pp. 431-478. Zbl0651.60077MR902778
11. P.J. Fitzsimmons, On a Connection Between Kuznetsov Processes and Quasi-Processes, Seminar on Stochastic Processes1987, pp. 123-133, Birkhäuser, Boston, 1988. Zbl0644.60075MR1046413
12. P.J. Fitzsimmons, Penetration Times and Skorohod Stopping, Séminaire de Probabilités XXII; Lecture Notes in Mathematics, No. 1321, pp. 166-174, Springer Verlag, Berlin-Heidelberg-New York, 1988. Zbl0644.60076MR960524
13. [FG] P.J. Fitzsimmons and R.K. Getoor, On the Potential Theory of Symmetric Markov Processes, Math. Annalen, Vol. 281, 1988, pp. 495-512. Zbl0627.60067MR954155
14. [FM] P.J. Fitzsimmons and B. Maisonneuve, Excessive Measures and Markov Processes with Random Birth and Death, Probab. Th. Rel. Fields, Vol. 72, 1986, pp. 319- 336. Zbl0584.60085MR843498
15. [Fu] M. Fukushima, Potential Theory of Symmetric Markov Processes and its Applications, Proc. Third Japan-U.S.S.R. Symp. Probab. Theory; Lecture Notes in Mathematics, No. 550, pp. 119-133, Springer Verlag, Berlin-Heidelberg-New York, 1976. Zbl0349.60077MR494514
16. [GHR] D. Geman, J. Horowitz and J. Rosen, A Local Time Analysis of Intersections of Brownian Paths in the Plane, Ann. Probab., Vol. 12, 1984, pp. 86-107. Zbl0536.60046MR723731
17. [G] R.K. Getoor, On the Construction of Kernels, Séminaire de Probabilités IX; Lecture Notes in Mathematics, No. 465, pp. 443-463, Springer Verlag, Berlin- Heidelberg-New York, 1975. Zbl0321.60056MR436342
18. [GSh] R.K. Getoor and M.J. Sharpe, Naturality, Standardness, and Weak Duality for Markov Processes, Z. Wahrscheinlichkeitstheorie verw. Geb., Vol. 67, 1984, pp. 1- 62. Zbl0553.60070MR756804
19. [GSt] R.K. Getoor and J. Steffens, The Energy Functional, Balayage, and Capacity, Ann. Inst. Henri Poincaré, Vol. 23, 1987, pp. 321-357. Zbl0617.60073MR898499
20. [H] J. Hawkes, Multiple Points for Symmetric Lévy Processes, Math. Proc. Cambridge Philos. Soc., Vol. 86, 1978, pp. 83-90. Zbl0396.60067MR464385
21. J. Hawkes, Potential Theory of Lévy Processes, Proc. London Math. Soc., Vol. 38, 1979, pp. 335-352. Zbl0401.60069MR531166
22. [HT] W.J. Hendricks and S.J. Taylor, Concerning Some Problems About Polar Sets for Processes with Stationary Independent Increments, Unpublished, 1976. 
23. [K] S.E. Kuznetsov, Construction of Markov Processes with Random Times of Birth and Death, Th. Probab. Appl., Vol. 18, 1974, pp. 571-574. Zbl0296.60049
24. [L] J.F. Le Gall, Sur le temps local d'intersection du mouvement Brownien plan et la méthode de renormalisation de Varadhan, Séminaire de Probabilités XIX; Lecture Notes in Mathematics, No. 1123, pp. 314-331, Springer Verlag, Berlin-Heidelberg- New York, 1985. Zbl0563.60072MR889492
25. [LRS] J.F. Le Gall, J.S. Rosen and N.R. Shieh, Multiple Points of Levy Processes, Ann. Probab., Vol. 17, 1989, pp. - . Zbl0684.60057MR985375
26. [MZ] E. Merzbach and M. Zakai, Predictable and Dual Predictable Projections of Two-parameter Stochastic Processes, Z. Wahrscheinlichkeitstheorie verw. Geb., Vol. 53, 1980, pp. 263-269. Zbl0437.60040MR586018
27. [M] P.-A. Meyer, Une remarque sur le calcul stochastique dépendant d'un paramètre, Séminaire de Probabilités XIII; Lect. Notes in Math., No. 721, Springer Verlag, Berlin-Heidelberg-New York, 1978. Zbl0407.60061
28. [P-S] Z.R. Pop-Stojanovic, Energy in Markov Processes, Functional Analysis II; Lecture Notes in Mathematics, No. 1242, pp. 374-395, Springer Verlag, Berlin-Heidelberg- New York, 1987. Zbl0625.60085MR906274
29. [P-SR] Z.R. Pop-Stojanovic and K.M. Rao, Convergence in Energy, Z. Wahrscheinlichkeitstheorie verw. Geb., 69, 1985, pp. 593-608. Zbl0548.60073MR791914
30. [Ra] K.M. Rao, On Polar Sets for Lévy Processes, J. London Math. Soc., Vol. 35, 1987, pp. 569-576. Zbl0587.60072MR889378
31. [Ro] L.C.G. Rogers, Multiple Points of Markov Processes in a Complete Metric Space, preprint, 1989. Zbl0746.60074
32. [Ta] S.J. Taylor, The Measure Theory of Random Fractals, Math. Proc. Cambridge Philos. Soc., Vol. 100, 1986, pp. 383-406. Zbl0622.60021MR857718
33. [To] N. Tongring, MultiplePoints of Brownian Motion, Conference in Modern Analysis and Probability, Contemporary Mathematics, Vol. 26, Amer. Math. Soc., Providence, 1984. Zbl0534.60071MR737416
34. N. Tongring, Which Sets Contain Multiple Points of Brownian Motion?, Math. Proc. Cambridge Philos. Soc., Vol. 103, 1988, pp. 181-187. Zbl0659.60114MR913461
35. [V] S.R.S. Varadhan, Appendix to "Euclidean Quantum Field Theory", by K. Symanzik, in Local Quantum Theory, R. JOST Ed., Academic Press, New York, 1969. 
36. [WM] J.B. Walsh and P.-A. Meyer, Quelques applications des résolventes de Ray, Invent. Math., Vol. 14, 1971, pp. 143-166. Zbl0224.60037MR295436

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