Lévy processes, pseudo-differential operators and Dirichlet forms in the Heisenberg group

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1. [1] Applebaum ( D.), Kunita ( H.). - Lévy flows on manifolds and Lévy processes on Lie groups, J. Math Kyoto Univ33, 1103-23 (1993). Zbl0804.58057MR1251218
2. [2] Applebaum ( D. ). — Lévy processes in stochastic differential geometry in Lévy Processes: Theory and Applications ed. O.Barndorff-Nielsen, T. Mikosch , S. Resnick ( BirkhäuserBostonBaselBerlin), 111-39 (2001). Zbl0984.60056MR1833695
3. [3] Applebaum ( D.). - Operator-valued stochastic differential equations arising from unitary group representations, J. Theor. Prob.14, 61-76 (2001). Zbl0979.60059MR1822894
4. [4] Applebaum ( D.). - Compound Poisson processes and Lévy processes in groups and symmetric spaces, J. Theor. Prob.13, 383-425 (2000). Zbl0985.60047MR1777540
5. [5] Baldus ( F.). - Strongly elliptic operators in spectrally invariant Ψ(M,g)-classes and generators of Markov processes, Universität Mainz preprint (2001). 
6. [6] Baldus ( F.). - S(M, g)-Pseudo Differential Calculus with Spectral Invariance on Rn and Manifolds for Banach Function Spaces, Logos Verlag, Berlin (2001). Zbl0982.58020
7. [7] Bouleau ( N. ) , Hirsch ( F.). - Dirichlet Forms and Analysis on Wiener Space, Walter de Gruyter, Berlin , New York (1991). Zbl0748.60046MR1133391
8. [8] Courrège ( P.). - Sur la forme intégro-différentielle des operateurs de C∞k dans C satifaisant au principe du maximum , Sém. Théorie du Potential exposé2, 38 pp (1965/66 ). 
9. [9] Folland ( G.F. ). - Harmonic Analysis on Phase Space, Annals of Math. Studies122, Princeton University Press (1989). Zbl0682.43001MR983366
10. [10] Fukushima ( M. ), Oshima ( Y.), Takeda ( M.). - Dirichlet Forms and Symmetric Markov Processes, Walter de Gruyter, Berlin, New York (1994 ). Zbl0838.31001MR1303354
11. [11] Gaveau ( B. ). — Holonomie stochastique et représentations du groupe d'Heisenberg. C.R. Acad. Sc. Paris. t. 280, 571-573 (1975). Zbl0294.43013MR516955
12. [12] Glowacki ( P.). - Stable semigroups of measures on the Heisenberg group, Studia Math.79, 105-38 (1984). Zbl0563.43002MR783046
13. [13] Heyer ( H.). - Probability Measures on Locally Compact Groups, Springer-Verlag, Berlin- Heidelberg (1977). Zbl0376.60002MR501241
14. [14] Hoh ( W.). - A construction of jump type Markov processes on manifolds , (in preparation) (2001). 
15. [15] Howe ( R.). - On the role of the Heisenberg group in harmonic analysis , Bull. Amer. Math. Soc.3, 821-43 (1980). Zbl0442.43002MR578375
16. [16] Hulanicki ( A.). - The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators in the Heisenberg group, Studia Math56, 165-173 (1976). Zbl0336.22007MR418257
17. [17] Hunt ( G.A. ). - Semigroups of measures on Lie groups, Trans. Amer. Math. Soc.81, 264-93 (1956). Zbl0073.12402
18. [18] Jacob ( N.) , Schilling ( R.). - Lévy-type processes and pseudodifferential operators in Lévy Processes: Theory and Applications ed. O. Barndorff-Nielsen, T. Mikosch, S. Resnick ( BirkhäuserBostonBaselBerlin), 139-69 (2001). Zbl0984.60054MR1833696
19. [19] Jacob ( N. ). - Pseudo-differential Operators and Markov Processes, Akademie-Verlag, Mathematical Research vol 94, Berlin (1996). Zbl0860.60002MR1409607
20. [20] Kunita ( H. ). - Stable Lévy processes on nilpotent Lie groups, in Stochastic Analysis on Infinite Dimensional Spaces, Pitman Research Notes Vol. 310, 167-82 (1994). Zbl0814.60003MR1415667
21. [21] Ma ( Z.-M. ) , Röckner ( M.). - Introduction to the Theory of non-Symmetric Dirichlet Forms, Springer-Verlag, BerlinHeidelberg (1992 ). Zbl0826.31001
22. [22] Neuenschwander ( D.). - Probabilities on the Heisenberg Group - Limit Theorems and Brownian Motion, Springer-Verlag, BerlinHeidelberg (1996 ). Zbl0870.60007MR1439509
23. [23] Pap ( G.). — Construction of processes with stationary and independent increments in Lie groups, Archiv der Math.69, 146-55 (1997). Zbl0904.60008MR1458701
24. [24] Pap ( G.). - Fourier transform of symmetric Gauss measures on the Heisenberg group, Semigroup Forum, 64, 130-58 (2002). Zbl0989.60006MR1867200
25. [25] Protter ( P. ). - Stochastic Integration and Differential Equations, Springer-Verlag, BerlinHeidelberg (1992). Zbl0694.60047MR2020294
26. [26] Ramaswami ( S.). - Semigroups of measures on Lie groups, J. Indian Math. Soc.38, 175-89 (1974). Zbl0353.60017MR420130
27. [27] Sato ( K-I.). - Lévy Processes and Infinite Divisibility, Cambridge University Press (1999). 
28. [28] Siebert ( E.). — Fourier analysis and limit theorems for convolution semigroups on a locally compact group, Advances in Math.39, 111-54 (1981). Zbl0469.60014MR609202
29. [29] Taylor ( M.E. ). - Noncommutative Harmonic Analysis, American Math. Soc (1986). Zbl0604.43001MR852988
30. [30] Weyl ( H.). - Group Theory and Quantum Mechanics, Dover Publications (first published in German by Methuen and Co Ltd (1931)) (1950). 
31. [31] Yamoto ( Y. ).— Stochastic differential equations and nilpotent Lie algebras, Z. Wahrscheinlichkeitstheorie verw. Gebiete47, 213-29 (1979). Zbl0427.60069
32. [32] Yor ( M.). - Some Aspects of Brownian Motion, Part 1, LNM ETHZürich, Birkhäuser (1992). Zbl0779.60070