Lévy processes, pseudo-differential operators and Dirichlet forms in the Heisenberg group
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 13 (2004) no. 2, pp. 149-177.
@article{AFST_2004_6_13_2_149_0,
     author = {Applebaum, David and Cohen, Serge},
     title = {L\'evy processes, pseudo-differential operators and {Dirichlet} forms in the {Heisenberg} group},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {149--177},
     publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 13},
     number = {2},
     year = {2004},
     mrnumber = {2126741},
     zbl = {1075.60048},
     language = {en},
     url = {http://archive.numdam.org/item/AFST_2004_6_13_2_149_0/}
}
TY  - JOUR
AU  - Applebaum, David
AU  - Cohen, Serge
TI  - Lévy processes, pseudo-differential operators and Dirichlet forms in the Heisenberg group
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2004
SP  - 149
EP  - 177
VL  - 13
IS  - 2
PB  - Université Paul Sabatier, Institut de mathématiques
PP  - Toulouse
UR  - http://archive.numdam.org/item/AFST_2004_6_13_2_149_0/
LA  - en
ID  - AFST_2004_6_13_2_149_0
ER  - 
%0 Journal Article
%A Applebaum, David
%A Cohen, Serge
%T Lévy processes, pseudo-differential operators and Dirichlet forms in the Heisenberg group
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2004
%P 149-177
%V 13
%N 2
%I Université Paul Sabatier, Institut de mathématiques
%C Toulouse
%U http://archive.numdam.org/item/AFST_2004_6_13_2_149_0/
%G en
%F AFST_2004_6_13_2_149_0
Applebaum, David; Cohen, Serge. Lévy processes, pseudo-differential operators and Dirichlet forms in the Heisenberg group. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 13 (2004) no. 2, pp. 149-177. http://archive.numdam.org/item/AFST_2004_6_13_2_149_0/

[1] Applebaum ( D.), Kunita (H.). - Lévy flows on manifolds and Lévy processes on Lie groups, J. Math Kyoto Univ 33, 1103-23 (1993). | MR | Zbl

[2] Applebaum ( D. ). - Lévy processes in stochastic differential geometry in Lévy Processes: Theory and Applications ed. O.Barndorff-Nielsen, T. Mikosch , S. Resnick ( Birkhäuser Boston Basel Berlin), 111-39 (2001). | MR | Zbl

[3] Applebaum ( D.). - Operator-valued stochastic differential equations arising from unitary group representations, J. Theor. Prob. 14, 61-76 (2001). | MR | Zbl

[4] Applebaum ( D.). - Compound Poisson processes and Lévy processes in groups and symmetric spaces, J. Theor. Prob. 13, 383-425 (2000). | MR | Zbl

[5] Baldus (F.). - Strongly elliptic operators in spectrally invariant Ψ(M,g)-classes and generators of Markov processes, Universität Mainz preprint (2001).

[6] Baldus (F.). - S(M, g)-Pseudo Differential Calculus with Spectral Invariance on Rn and Manifolds for Banach Function Spaces, Logos Verlag, Berlin (2001). | Zbl

[7] Bouleau (N. ) , Hirsch ( F.). - Dirichlet Forms and Analysis on Wiener Space, Walter de Gruyter, Berlin , New York (1991). | MR | Zbl

[8] Courrège ( P.). - Sur la forme intégro-différentielle des operateurs de C∞k dans C satifaisant au principe du maximum , Sém. Théorie du Potential exposé 2, 38 pp (1965/66 ). | Numdam

[9] Folland (G.F. ). - Harmonic Analysis on Phase Space, Annals of Math. Studies 122, Princeton University Press (1989). | MR | Zbl

[10] Fukushima ( M. ), Oshima (Y.), Takeda (M.). - Dirichlet Forms and Symmetric Markov Processes, Walter de Gruyter, Berlin, New York (1994 ). | MR | Zbl

[11] Gaveau (B. ). - Holonomie stochastique et représentations du groupe d'Heisenberg. C.R. Acad. Sc. Paris. t. 280, 571-573 (1975). | MR | Zbl

[12] Glowacki ( P.). - Stable semigroups of measures on the Heisenberg group, Studia Math. 79, 105-38 (1984). | MR | Zbl

[13] Heyer (H.). - Probability Measures on Locally Compact Groups, Springer-Verlag, Berlin- Heidelberg (1977). | MR | Zbl

[14] Hoh (W.). - A construction of jump type Markov processes on manifolds , (in preparation) (2001).

[15] Howe (R.). - On the role of the Heisenberg group in harmonic analysis , Bull. Amer. Math. Soc. 3, 821-43 (1980). | MR | Zbl

[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 Math 56, 165-173 (1976). | MR | Zbl

[17] Hunt (G.A. ). - Semigroups of measures on Lie groups, Trans. Amer. Math. Soc. 81, 264-93 (1956). | Zbl

[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 ( Birkhäuser Boston Basel Berlin), 139-69 (2001). | MR | Zbl

[19] Jacob (N. ). - Pseudo-differential Operators and Markov Processes, Akademie-Verlag, Mathematical Research vol 94, Berlin (1996). | MR | Zbl

[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). | MR | Zbl

[21] Ma (Z.-M. ) , Röckner ( M.). - Introduction to the Theory of non-Symmetric Dirichlet Forms, Springer-Verlag, Berlin Heidelberg (1992 ). | Zbl

[22] Neuenschwander ( D.). - Probabilities on the Heisenberg Group - Limit Theorems and Brownian Motion, Springer-Verlag, Berlin Heidelberg (1996 ). | MR | Zbl

[23] Pap (G.). - Construction of processes with stationary and independent increments in Lie groups, Archiv der Math. 69, 146-55 (1997). | MR | Zbl

[24] Pap (G.). - Fourier transform of symmetric Gauss measures on the Heisenberg group, Semigroup Forum, 64, 130-58 (2002). | MR | Zbl

[25] Protter (P. ). - Stochastic Integration and Differential Equations, Springer-Verlag, Berlin Heidelberg (1992). | MR | Zbl

[26] Ramaswami ( S.). - Semigroups of measures on Lie groups, J. Indian Math. Soc. 38, 175-89 (1974). | MR | Zbl

[27] Sato (K-I.). - Lévy Processes and Infinite Divisibility, Cambridge University Press (1999).

[28] Siebert ( E.). - Fourier analysis and limit theorems for convolution semigroups on a locally compact group, Advances in Math. 39, 111-54 (1981). | MR | Zbl

[29] Taylor (M.E. ). - Noncommutative Harmonic Analysis, American Math. Soc (1986). | MR | Zbl

[30] Weyl (H.). - Group Theory and Quantum Mechanics, Dover Publications (first published in German by Methuen and Co Ltd (1931)) (1950).

[31] Yamoto (Y. ).- Stochastic differential equations and nilpotent Lie algebras, Z. Wahrscheinlichkeitstheorie verw. Gebiete 47, 213-29 (1979). | Zbl

[32] Yor (M.). - Some Aspects of Brownian Motion, Part 1, LNM ETH Zürich, Birkhäuser (1992). | Zbl