Quelques propriétés du mouvement brownien non-commutatif
Hommage à P. A. Meyer et J. Neveu, Astérisque, no. 236 (1996), pp. 73-101.
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     author = {Biane, P.},
     title = {Quelques propri\'et\'es du mouvement brownien non-commutatif},
     booktitle = {Hommage \`a P. A. Meyer et J. Neveu},
     series = {Ast\'erisque},
     pages = {73--101},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {236},
     year = {1996},
     mrnumber = {1417975},
     zbl = {0867.46043},
     language = {fr},
     url = {http://archive.numdam.org/item/AST_1996__236__73_0/}
}
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Biane, P. Quelques propriétés du mouvement brownien non-commutatif, dans Hommage à P. A. Meyer et J. Neveu, Astérisque, no. 236 (1996), pp. 73-101. http://archive.numdam.org/item/AST_1996__236__73_0/

[Ar] H. Araki, Factorisable representations of current algebras, Pub. R.I.M.S., Kyoto University, Ser. A, Vol. 5, n° 3, 1970, 361-422. | MR | Zbl

[At] K. B. Athreya et P. E. Ney, Branching processes, Springer-Verlag, New York, Berlin, Heidelberg, 1972. | MR | Zbl

[Bh] R. V. Bhat, K. R. Parthasarathy, Markov Dilations of Nonconservative Dynamical Semigroups and a Quantum Boundary theory, à paraître, Ann. I.H.P. | Numdam | MR | Zbl

[B1] P. Biane, Calcul stochastique non-commutatif, Lectures on Probability Theory, Lecture Notes in Mathematics 1608, Springer, 1995, 1-96. | MR | Zbl

[B2] P. Biane, Quantum random walks on the dual of SU(n), Prob. Th. and Rel. fields, 89, 1991, 117-129. | MR | Zbl

[Bo] P. Bougerol, Théorème central limite local sur certains groupes de Lie, Ann. Sc. Éc. Norm. Sup., 4e série, 14, 1981, p. 403 à 432. | DOI | EuDML | Numdam | MR | Zbl

[C-H] A. M. Cockroft et R. L. Hudson, Quantum mechanical Wiener processes, J. Multiv. Anal. 7, 1978, 107-124. | DOI | MR | Zbl

[D-M] C. Dellacherie et P. A. Meyer, Probabilités et Potentiel, Chapitres IX à XI, Hermann, Paris, 1983. | MR | Zbl

[Di] J. Dixmier, Les C * -algèbres et leurs représentations, Gauthiers Villars, Paris, 1964. | MR | Zbl

[Do] J. L. Doob, Classical Potential theory and its Probabilistic Counterpart, Springer-Verlag, New York, Berlin, Heidelberg, 1984. | MR | Zbl

[F] J. Faraut, Analyse harmonique et fonctions spéciales, in J. Faraut, K. Harzalah, Deux cours d'analyse harmonique, Progress in Mathematics, vol. 69, Birkhäuser, Basel 1987. | MR | Zbl

[H-P] R. L. Hudson et K. R. Parthasarathy, Quantum Ito's fromula and stochastic evolutions, Comm. Math. Phys., 93, 1984, 301-323. | DOI | MR | Zbl

[I-M] K. Ito et H. P. Mackean, Diffusion processes and their sample paths, Springer Verlag, New York, Heidelberg, Berlin, 1974 | MR

[L] R. Y. Lee, Field algebras of operator fields trivial except at one point, Indiana Univ. Math. J. 26 (1977) 351-372. | DOI | MR | Zbl

[M1] P. A. Meyer, Eléments de Probabilités Quantiques, Séminaire de Probabilités XX, Lecture Notes in Mathematics 1204, Springer, 1986, 186-312. | EuDML | Numdam | MR | Zbl

[M2] P. A. Meyer, Quantum Probability for probabilists, Lecture Notes in Mathematics 1538, Springer, 1993 | MR | Zbl

[O] L. Overbeck, Martin boundaries of some branching processes, Ann. I.H.P. 30, 2, (1994), 181-196. | EuDML | Numdam | MR | Zbl

[P] K. R. Parthasarathy, An Introduction to Quantum Stochastic Calculus, Monographs in Mathematics, Vol. 85, Birkhäuser, Basel, 1992. | MR | Zbl

[P2] K. R. Parthasarathy, A generalized Biane's process, Séminaire de Probabilités XXIV, Lecture Notes in Mathematics 1426, Springer, 1990, 345-348. | EuDML | Numdam | MR | Zbl

[P-S] K. R. Parthasarathy et K. Schmidt, Positive definite kernels, Continuous Tensor Products, and Central Limit Theorems of Probability Theory, Lecture Notes in Mathematics 272, Springer, 1972. | MR | Zbl

[Sa] J. L. Sauvageot, Markov quantum semi-groups admit covariant markov C * -dilations, Comm. Math. Phys. 106, 1986, 91-103. | DOI | MR | Zbl

[Sc] M. Schürmann, White noise on bialgebras, Lecture Notes in Mathematics 1544, Springer, 1993. | MR | Zbl

[S-Z] S. Stratila et L. Zsido, Lectures on von Neumann algebras, Abacus press, Turnbridge Wells, 1979. | MR | Zbl

[Tak] M. Takesaki, Conditionnai expectations in von Neumann algebras, J. Funct. Anal. 9, 1972, 306-321. | DOI | MR | Zbl

[Tay] M. E. Taylor, Non commutative harmonic analysis, Mathematical surveys and monographs, 22, A.M.S. Providence, 1986. | MR | Zbl

[V] D. Voiculescu, Remarks on the singular extension in the C * -algebra of the Heisenberg group, J. Operator Theory 5 (1981) 147-170. | MR | Zbl

[vWl] W. Von Waldenfels, Spontaneous light emission described by a quantum stochastic differential equation, Quantum Probability and applications II, Lecture Notes in Mathematics 1136, Springer Berlin, Heidelberg, New York, 1985, 361-374. | MR | Zbl

[vW2] W. Von Waldenfels, The inverse oscillator in a heat bath as a quantum stochastic process, preprint, Heidelberg, 1994.

[W] D. Widder, The heat equation, Academic Press, New York, 1975. | MR | Zbl