Markovian bridges and reversible diffusion processes with jumps

 Access to full text

 Full (PDF)

1. [1] S. Albeverio, J. Rezende, J.-C. Zambrini, Probability and quantum symmetries II. The theorem of Noether in quantum mechanics, submitted for publication. Zbl1112.81072
2. [2] S. Albeverio, K. Yasue, J.-C. Zambrini, Euclidean quantum mechanics: analytical approach, Ann. Inst. H. Poincaré Phys. Théor.50 (3) (1989) 259-308. Zbl0687.60091MR1017966
3. [3] S. Bernstein, Sur les liaisons entre les grandeurs aléatoires, Verh. des intern. Mathematikerkongr., vol. 1, 1932, Zürich. Zbl0007.02104JFM58.1157.04
4. [4] J. Bertoin, Lévy Processes, Cambridge Tracts in Mathematics, vol. 121, Cambridge Univ. Press, 1998. Zbl0938.60005MR1406564
5. [5] A. Beurling, An automorphism of product measures, Ann. of Math. (2)72 (1960) 189-200. Zbl0091.13001MR125424
6. [6] P. Cattiaux, Time reversal of diffusion processes with a boundary condition, Stochastic Process. Appl.28 (2) (1988) 275-292. Zbl0652.60083MR952834
7. [7] P. Cattiaux, C. Léonard, Large deviations and Nelson processes, Forum Math.7 (1) (1995) 95-115. Zbl0817.60021MR1307957
8. [8] K.L. Chung, J.-C. Zambrini, Introduction to Random Times and Quantum Randomness, World Scientific, 2003. Zbl1041.81074MR1999000
9. [9] A.B. Cruzeiro, L. Wu, J.-C. Zambrini, Bernstein processes associated with a Markov process, in: Stochastic Analysis and Mathematical Physics (Santiago, 1998), Birkhäuser Boston, Boston, MA, 2000, pp. 41-72. Zbl0965.60101MR1764785
10. [10] R.L. Dobrushin, Yu.M. Sukhov, Ĭ. Fritts, A.N. Kolmogorov—founder of the theory of reversible Markov processes, Uspekhi Mat. Nauk.43 (6(264)) (1988) 167-188. Zbl0669.60001MR983882
11. [11] J.L. Doob, Classical Potential Theory and its Probabilistic Counterpart, Springer-Verlag, Berlin, 1984. Zbl0990.31001MR731258
12. [12] M. Emery, M. Yor, A parallel between Brownian bridges and gamma bridges, Prépublication No 846, Laboratoire de Probabilités de l'Université Paris VI, 2003. MR2074696
13. [13] S.N. Ethier, T.G. Kurtz, Markov Processes, Characterization and Convergence, Wiley, New York, 1986. Zbl0592.60049MR838085
14. [14] P. Fitzsimmons, J. Pitman, M. Yor, Markovian bridges: Construction, Palm interpretation, and splicing, in: Cinlar E., (Eds.), Seminar on Stochastic Processes, Prog. Probab., vol. 33, Birkhäuser, Washington, 1992, pp. 101-134. Zbl0844.60054MR1278079
15. [15] W.H. Fleming, H.M. Soner, Controlled Markov Processes and Viscosity Solutions, Springer-Verlag, New York, 1993. Zbl0773.60070MR1199811
16. [16] J.M. Hammersley, Harnesses, in: Proc. Fifth Berkeley Sympos. Mathematical Statistics and Probability (Berkeley, Calif., 1965/66), vol. III: Physical Sciences, Univ. California Press, Berkeley, CA, 1967, pp. 89-117. Zbl0189.27705MR224144
17. [17] F. Hirsch, Opérateurs carré du champ (d'après J.P. Roth), in: Séminaire Bourbaki, 29e année (1976/77), Lecture Notes in Math., vol. 677, Springer, Berlin, 1978, pp. 167-182. Zbl0389.31005MR521767
18. [18] G.A. Hunt, Markoff chains and Martin boundaries, Illinois J. Math.4 (1960) 313-340. Zbl0094.32103MR123364
19. [19] T. Ichinose, S. Takanobu, The norm estimate of the difference between the Kac operator and Schrödinger semigroup. II. The general case including the relativistic case, Electron. J. Probab.5 (4) (2000) 47, (electronic). Zbl0987.47032MR1743725
20. [20] N. Ikeda, S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, 1989. Zbl0684.60040MR1011252
21. [21] N. Jacob, R.L. Schilling, Lévy-type processes and pseudodifferential operators, in: Resnick S., Barndorff-Nielsen O., Mikosch Th. (Eds.), Lévy Processes, Birkhäuser Boston, Boston, MA, 2001, pp. 139-168. Zbl0984.60054MR1833696
22. [22] J. Jacod, Calcul stochastique et problèmes de martingales, Lecture Notes in Mathematics, vol. 714, Springer-Verlag, Berlin, 1979. Zbl0414.60053MR542115
23. [23] J. Jacod, P. Protter, Time reversal on Lévy processes, Ann. Probab.16 (2) (1988) 620-641. Zbl0646.60052MR929066
24. [24] B. Jamison, Reciprocal processes, Z. Wahr. Verw. Geb.30 (1974) 65-86. Zbl0326.60033MR359016
25. [25] T. Komatsu, Markov processes associated with certain integro-differential operators, Osaka J. Math.10 (1973) 271-303. Zbl0284.60066MR359017
26. [26] J.-P. Lepeltier, B. Marchal, Problème des martingales et équations différentielles stochastiques associées à un opérateur intégro-différentiel, Ann. Inst. H. Poincaré Sect. B (N.S.)12 (1) (1976) 43-103. Zbl0345.60029MR413288
27. [27] N. Privault, J.-C. Zambrini, Euclidean quantum mechanics in the momentum representation, 2004, in preparation. Zbl1076.81030MR2125554
28. [28] J.P. Roth, Opérateurs carré du champ et formule de Lévy–Kinchine sur les espaces localement compacts, C. R. Acad. Sci. Paris Sér. A278 (1974) 1103-1106. Zbl0282.47010
29. [29] S.J. Sheu, Stochastic control and exit probabilities of jump processes, SIAM J. Control Optim.23 (2) (1985) 306-328. Zbl0567.60032MR777462
30. [30] D. Stroock, Diffusion processes associated with Lévy generators, Z. Wahr. Verw. Geb.32 (3) (1975) 209-244. Zbl0292.60122MR433614
31. [31] J.-C. Zambrini, Variational processes and stochastic versions of mechanics, J. Math. Phys.27 (9) (1986) 2307-2330. Zbl0623.60102MR854761