Quantum stochastic calculus for the uniform measure and Boolean convolution
Séminaire de probabilités de Strasbourg (2001)
- Volume: 35, page 28-47
 
Access Full Article
topHow to cite
topPrivault, Nicolas. "Quantum stochastic calculus for the uniform measure and Boolean convolution." Séminaire de probabilités de Strasbourg 35 (2001): 28-47. <http://eudml.org/doc/114068>.
@article{Privault2001,
	author = {Privault, Nicolas},
	journal = {Séminaire de probabilités de Strasbourg},
	keywords = {Boolean Fock space; noncommutative processes; combinations of annihilators and creators; Boolean Brownian and Poisson processes; Bernoulli processes},
	language = {eng},
	pages = {28-47},
	publisher = {Springer - Lecture Notes in Mathematics},
	title = {Quantum stochastic calculus for the uniform measure and Boolean convolution},
	url = {http://eudml.org/doc/114068},
	volume = {35},
	year = {2001},
}
TY  - JOUR
AU  - Privault, Nicolas
TI  - Quantum stochastic calculus for the uniform measure and Boolean convolution
JO  - Séminaire de probabilités de Strasbourg
PY  - 2001
PB  - Springer - Lecture Notes in Mathematics
VL  - 35
SP  - 28
EP  - 47
LA  - eng
KW  - Boolean Fock space; noncommutative processes; combinations of annihilators and creators; Boolean Brownian and Poisson processes; Bernoulli processes
UR  - http://eudml.org/doc/114068
ER  - 
References
top- [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. Zbl0878.60041MR1383121
 - [2] Ph. Biane. Processes with free increments. Math. Z., 227(1):143-174, 1998. Zbl0902.60060MR1605393
 - [3] M. Bozejko. Positive definite functions on the free group and the noncommutative Riesz product. Boll. Unione Mat. Ital., A5:13-21, 1986. Zbl0591.43009MR833375
 - [4] W. Feller. An introduction to probability theory and its applications. Vol. II. John Wiley & Sons Inc., New York, 1966. Zbl0138.10207
 - [5] J.M. Lindsay. Quantum and non-causal stochastic calculus. Probab. Theory Related Fields, 97:65-80, 1993. Zbl0794.60052
 - [6] M. Métivier. Semimartingales: a Course on Stochastic Processes. de Gruyter, 1982. Zbl0503.60054MR688144
 - [7] P.A. Meyer. Quantum Probability for Probabilists, volume 1538 of Lecture Notes in Mathematics. Springer-Verlag, 1993. Zbl0773.60098MR1222649
 - [8] A.F. Nikiforov and V.B. Uvarov. Special Functions of Mathematical Physics. Birkäuser, 1988. Zbl0624.33001MR922041
 - [9] K.R. Parthasarathy. An Introduction to Quantum Stochastic Calculus. Birkäuser, 1992. Zbl0751.60046MR1164866
 - [10] N. Privault. A different quantum stochastic calculus for the Poisson process. Probab. Theory Related Fields, 105:255-278, 1996. Zbl0849.60056MR1392454
 - [11] N. Privault. Calcul des variations stochastique pour la mesure de densité uniforme. Potential Analysis, 7(2):577-601, 1997. Zbl0894.60047MR1467207
 - [12] G. Sansone. Orthogonal Functions, Revised English Edition. Interscience publishers, New York, 1959. Zbl0084.06106MR103368
 - [13] M. Schürmann. Direct sums of tensor products and non-commutative independence. J. Funct. Anal., 133(1):1-9, 1995. Zbl0868.46048MR1351638
 - [14] R. Speicher. A new example of "independence" and "white noise". Probab. Theory Related Fields, 84:141-159, 1990. Zbl0671.60109MR1030725
 - [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. Zbl0872.46033MR1426845
 - [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. Zbl0795.46049MR1217253
 
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.