Quantum stochastic calculus for the uniform measure and Boolean convolution
Séminaire de probabilités de Strasbourg, Tome 35 (2001), pp. 28-47. 
@article{SPS_2001__35__28_0,
     author = {Privault, Nicolas},
     title = {Quantum stochastic calculus for the uniform measure and {Boolean} convolution},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     pages = {28--47},
     publisher = {Springer - Lecture Notes in Mathematics},
     volume = {35},
     year = {2001},
     mrnumber = {1837275},
     zbl = {0981.81044},
     language = {en},
     url = {http://www.numdam.org/item/SPS_2001__35__28_0/}
}
TY  - JOUR
AU  - Privault, Nicolas
TI  - Quantum stochastic calculus for the uniform measure and Boolean convolution
JO  - Séminaire de probabilités de Strasbourg
PY  - 2001
SP  - 28
EP  - 47
VL  - 35
PB  - Springer - Lecture Notes in Mathematics
UR  - http://www.numdam.org/item/SPS_2001__35__28_0/
LA  - en
ID  - SPS_2001__35__28_0
ER  - 
%0 Journal Article
%A Privault, Nicolas
%T Quantum stochastic calculus for the uniform measure and Boolean convolution
%J Séminaire de probabilités de Strasbourg
%D 2001
%P 28-47
%V 35
%I Springer - Lecture Notes in Mathematics
%U http://www.numdam.org/item/SPS_2001__35__28_0/
%G en
%F SPS_2001__35__28_0
Privault, Nicolas. Quantum stochastic calculus for the uniform measure and Boolean convolution. Séminaire de probabilités de Strasbourg, Tome 35 (2001), pp. 28-47. http://www.numdam.org/item/SPS_2001__35__28_0/

[1] Ph. Biane. Calcul stochastique non-commutatif. In Ecole d'été de Probabilités de Saint-Flour, volume 1608 of Lecture Notes in Mathematics. Springer-Verlag, 1993. | MR | Zbl

[2] Ph. Biane. Processes with free increments. Math. Z., 227(1):143-174, 1998. | MR | Zbl

[3] M. Bozejko. Positive definite functions on the free group and the noncommutative Riesz product. Boll. Unione Mat. Ital., A5:13-21, 1986. | MR | Zbl

[4] W. Feller. An introduction to probability theory and its applications. Vol. II. John Wiley & Sons Inc., New York, 1966.

[5] J.M. Lindsay. Quantum and non-causal stochastic calculus. Probab. Theory Related Fields, 97:65-80, 1993. | Zbl

[6] M. Métivier. Semimartingales: a Course on Stochastic Processes. de Gruyter, 1982. | MR | Zbl

[7] P.A. Meyer. Quantum Probability for Probabilists, volume 1538 of Lecture Notes in Mathematics. Springer-Verlag, 1993. | MR | Zbl

[8] A.F. Nikiforov and V.B. Uvarov. Special Functions of Mathematical Physics. Birkäuser, 1988. | MR | Zbl

[9] K.R. Parthasarathy. An Introduction to Quantum Stochastic Calculus. Birkäuser, 1992. | MR | Zbl

[10] N. Privault. A different quantum stochastic calculus for the Poisson process. Probab. Theory Related Fields, 105:255-278, 1996. | MR | Zbl

[11] N. Privault. Calcul des variations stochastique pour la mesure de densité uniforme. Potential Analysis, 7(2):577-601, 1997. | MR | Zbl

[12] G. Sansone. Orthogonal Functions, Revised English Edition. Interscience publishers, New York, 1959. | MR | Zbl

[13] M. Schürmann. Direct sums of tensor products and non-commutative independence. J. Funct. Anal., 133(1):1-9, 1995. | MR | Zbl

[14] R. Speicher. A new example of "independence" and "white noise". Probab. Theory Related Fields, 84:141-159, 1990. | MR | Zbl

[15] R. Speicher and R. Woroudi. Boolean convolution. In D. Voiculescu, editor, Free probability theory. Papers from a workshop on random matrices and operator algebra free products, volume 12 of Fields Inst. Commun., pages 267-279, Toronto, 1995. American Mathematical Society. | MR | Zbl

[16] D. Voiculescu, K. Dykema, and A. Nica. Free random variables. A noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups, volume 1 of CRM Monograph Series. American Mathematical Society, Providence, RI, 1992. | MR | Zbl