Capacity and energy for multiparameter Markov processes
Fitzsimmons, P. J. ; Salisbury, Thomas S.
Annales de l'I.H.P. Probabilités et statistiques, Tome 25 (1989), p. 325-350 / Harvested from Numdam
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@article{AIHPB_1989__25_3_325_0,
     author = {Fitzsimmons, Patrick J. and Salisbury, Thomas S.},
     title = {Capacity and energy for multiparameter Markov processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {25},
     year = {1989},
     pages = {325-350},
     mrnumber = {1023955},
     zbl = {0689.60071},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_1989__25_3_325_0}
}

Fitzsimmons, P. J.; Salisbury, Thomas S. Capacity and energy for multiparameter Markov processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 25 (1989) pp. 325-350. http://gdmltest.u-ga.fr/item/AIHPB_1989__25_3_325_0/

[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. | Numdam | MR 381010 | Zbl 0231.60066

[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. | MR 606006 | Zbl 0431.60057

[BG] R.M. Blumenthal and R.K. Getoor, Markov Processes and Potential Theory, Academic Press, New York, 1968. | MR 264757 | Zbl 0169.49204

[DM] C. Dellacherie and P.-A. Meyer, Probabilités et Potentiel, Ch. V-VII, Hermann, Paris, 1980. | MR 488194 | Zbl 0464.60001

C. Dellacherie and P.-A. Meyer, Probabilités et Potentiel, Ch. XII-XVI, Hermann, Paris, 1987. | MR 488194

[D] E.B. Dynkin, Markov Systems and their Additive Functionals, Ann. Probab., Vol. 5, 1977, pp. 653-677. | MR 451415 | Zbl 0379.60076

E.B. Dynkin, Additive Functionals of Several Time-Reversible Markov Processes, J. Funct. Anal., Vol. 42, 1981, pp. 64-101. | MR 620580 | Zbl 0467.60069

[E] S.N. Evans, Multiple Points in the Sample Paths of a Lévy Process, Probab. Th. Rel. Fields, Vol. 76, 1987, pp. 359-367. | MR 912660

S.N. Evans, Potential Theory for a Family of Several Markov Processes, Ann. Inst. Henri Poincaré, Vol. 23, 1987, pp. 499-530. | Numdam | MR 906728 | Zbl 0625.60086

[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. | MR 902778 | Zbl 0651.60077

P.J. Fitzsimmons, On a Connection Between Kuznetsov Processes and Quasi-Processes, Seminar on Stochastic Processes 1987, pp. 123-133, Birkhäuser, Boston, 1988. | MR 1046413 | Zbl 0644.60075

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. | Numdam | MR 960524 | Zbl 0644.60076

[FG] P.J. Fitzsimmons and R.K. Getoor, On the Potential Theory of Symmetric Markov Processes, Math. Annalen, Vol. 281, 1988, pp. 495-512. | MR 954155 | Zbl 0627.60067

[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. | MR 843498 | Zbl 0584.60085

[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. | MR 494514 | Zbl 0349.60077

[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. | MR 723731 | Zbl 0536.60046

[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. | Numdam | MR 436342 | Zbl 0321.60056

[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. | MR 756804 | Zbl 0553.60070

[GSt] R.K. Getoor and J. Steffens, The Energy Functional, Balayage, and Capacity, Ann. Inst. Henri Poincaré, Vol. 23, 1987, pp. 321-357. | Numdam | MR 898499 | Zbl 0617.60073

[H] J. Hawkes, Multiple Points for Symmetric Lévy Processes, Math. Proc. Cambridge Philos. Soc., Vol. 86, 1978, pp. 83-90. | MR 464385 | Zbl 0396.60067

J. Hawkes, Potential Theory of Lévy Processes, Proc. London Math. Soc., Vol. 38, 1979, pp. 335-352. | MR 531166 | Zbl 0401.60069

[HT] W.J. Hendricks and S.J. Taylor, Concerning Some Problems About Polar Sets for Processes with Stationary Independent Increments, Unpublished, 1976.

[K] S.E. Kuznetsov, Construction of Markov Processes with Random Times of Birth and Death, Th. Probab. Appl., Vol. 18, 1974, pp. 571-574. | Zbl 0296.60049

[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. | Numdam | MR 889492 | Zbl 0563.60072

[LRS] J.F. Le Gall, J.S. Rosen and N.R. Shieh, Multiple Points of Levy Processes, Ann. Probab., Vol. 17, 1989, pp. - . | MR 985375 | Zbl 0684.60057

[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. | MR 586018 | Zbl 0437.60040

[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. | Numdam | Zbl 0407.60061

[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. | MR 906274 | Zbl 0625.60085

[P-SR] Z.R. Pop-Stojanovic and K.M. Rao, Convergence in Energy, Z. Wahrscheinlichkeitstheorie verw. Geb., 69, 1985, pp. 593-608. | MR 791914 | Zbl 0548.60073

[Ra] K.M. Rao, On Polar Sets for Lévy Processes, J. London Math. Soc., Vol. 35, 1987, pp. 569-576. | MR 889378 | Zbl 0587.60072

[Ro] L.C.G. Rogers, Multiple Points of Markov Processes in a Complete Metric Space, preprint, 1989. | Numdam | Zbl 0746.60074

[Ta] S.J. Taylor, The Measure Theory of Random Fractals, Math. Proc. Cambridge Philos. Soc., Vol. 100, 1986, pp. 383-406. | MR 857718 | Zbl 0622.60021

[To] N. Tongring, Multiple Points of Brownian Motion, Conference in Modern Analysis and Probability, Contemporary Mathematics, Vol. 26, Amer. Math. Soc., Providence, 1984. | MR 737416 | Zbl 0534.60071

N. Tongring, Which Sets Contain Multiple Points of Brownian Motion?, Math. Proc. Cambridge Philos. Soc., Vol. 103, 1988, pp. 181-187. | MR 913461 | Zbl 0659.60114

[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.

[WM] J.B. Walsh and P.-A. Meyer, Quelques applications des résolventes de Ray, Invent. Math., Vol. 14, 1971, pp. 143-166. | MR 295436 | Zbl 0224.60037