Processes with free increments

Mathematische Zeitschrift

Volumn 227, Issue 1, 1998, Pages 143-174

  Biane, Philippe ^a,b  

^a University of Paris VII LPSM partially supported by ERC Starting Grant 680275 MALIG   (France)

^b ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032330569     PISSN: 00255874     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00004363     Document Type: Article

References (31)

1. J. Azéma: Sur les fermés aléatoires, Sém. Proba. XIX, Lecture Notes in Math. 1123. Springer, Berlin, 1985, pp. 397-495
2. H. Bercovici, D. Voiculescu: Lévy-Hinchin type theorems for multiplicative and additive free convolution. Pacific J. Math. 153 (1992), 217-248
3. H. Bercovici, D. Voiculescu: Free convolution of, measures with unbounded support. Indiana University Mathematics Journal 42 (1993), 733-773
4. B. R. Bhat, K. R. Parthasarathy: Markov, dilations of nonconservative dynamical semi-groups and a quantum boundary theory Ann. Inst. H. Poincaré 31 (1995), 601-652
5. P. Biane: Quelques propriétés du mouvement brownien non-commutatif. Astérisque, SMF (to appear)
6. M. Bozejko, B. Kümmerer, R. Speicher: q-gaussian processes: non-commutative and classical aspects, Preprint (1995)
7. H. Cartan: Sur les groupes de transformations analytiques. Œuvres Tome 1, Springer, Berlin, 1979
8. K.L. Chung: Lectures from Markov processes to brownian motion. Grund. Math. Wiss. 249, Springer, Berlin, 1982
9. J.L. Doob: Stochastic processes. Wiley and Sons, New York, 1953
10. C Dellacherie, P.A. Meyer: Probabilités et potentiel, Tomes 3 et 4, Hermann, Paris
11. M. Émery: On the Azéma martingales. Séminaire de probabilités XXIII Lect. Notes in Math. 1372, Springer, Berlin, 1990, pp. 66-87
12. B. Kümmerer: Markov dilations on W*-algebras Journ. Funct. Anal. 63 (1985) 139-177
13. H. Maassen: Addition of freely independent random variables. Journ. Funct. Anal. 106 (1992), 409-438
14. M. Montgomery, L. Zippin: Transformation groups Interscience tracts in pure and applied mathematics, No 1, Interscience, New York, 1955
15. P. Neu, R. Speicher: Rigourous meanfield model for CPA: Anderson model with free random variables. J. Stat. Phys. 80 (1995), 1279-1308
16. A. Nica: A one parameter family of transforms linearizing convolution laws for probability distributions. Comm. Math. Phys. 168 (1995), 187-207
17. A. Nica, R. Speicher: A "Fourier transform" for multiplicative functions on non-crossing partitions. (1994) (to appear)
18. K. R. Parthasarathy: Azéma martingales, quantum stochastic calculus. Proc. R. C. Bose Symposium, Wiley Eastern, 1990, pp. 551-569
19. K. R. Parthasarathy: An introduction to quantum stochastic: calculus. Monographs in Mathematics, Vol. 85, Birkhaüser, Basel, 1992
20. D. Revuz, M. Yor: Continuous martingale calculus. Grund. Math. Wiss. 293, Springer, Berlin, 1991
21. J.L. Sauvageot: Markov quantum semi-groups admit covariant Markov C*-dilations. Comm. Math. Phys 106 (1986), 91-103
22. [Sc] M. Schürmann: The Azéma martingales as, components of quantum independent increments processes. Séminaire de probabilités XXV, Lect. Notes. in Math. 1485, Springer, Berlin, 1991 24-30
23. R. Speicher: A new example of "independence" and "white noise". Prob. Th. Rel. Fields 84 (1990), 141-159
24. R. Speicher: Multiplicative functions on the lattice of non-crossing partitions and free convolution. Math. Annalen 298 (1994), 611-628
25. R. Speicher: Combinatorial theory of the free product with amalgamation and operator-valued free probability theory, Habilitationsschrift, Heidelberg, 1994
26. [T] M. Takesaki: Conditional expectation in von Neumann algebra. Journ. Funct. Anal. 9 (1972), 306-321
27. D. Voiculescu: Addition of certain non-commutative random variables. Journ. Funct. Anal. 66 (1986), 323-346
28. D. Voiculescu: Multiplication of certain non-commutative random variables. Journ. Operator Theory 18 (1987), 223-235
29. D. Voiculescu: The analogues of entropy and Fisher's information measure in free probability theory, I. Commun. Math. Phys. 155 (1993), 71-92
30. D. Voiculescu, K. Dykema, A. Nica: Free random variables. CRM Monograph Series No. 1, Amer. Math. Soc., Providence, RI, 1992
31. [Z] V.M. Zolotarev: One-dimensional stable distributions. Translations of mathematical monographs, vol 65, Amer. Math. Soc. Providence, RI, 1986