References
Abe, E.: Hopf algebras. Cambridge: University Press 1980
Accardi, L.: Non-relativistic quantum mechanics as a non-commutative Markov process. Adv. Math.20, 329–366 (1976)
Accardi, L., Parthasarathy, K.R.: A martingale characterisation of canonical commutation and anticommutation relations, submitted for publication
Accardi, L., Frigerio, A., Lewis, J.T.: Quantum stochastic processes. Publ. RIMS, Kyoto Univ.18, 97–133 (1982)
Applebaum, D.: The strong Markov property for Fermion Brownian motion. J. Funct. Anal.65, 273–291 (1986)
Applebaum, D., Hudson, R.L.: Fermion Ito's formula and stochastic evolutions. Commun. Math. Phys.96, 473–496 (1984)
Bourbaki, N.: Eléments de mathématique. Théorie des ensembles. Paris: Hermann 1970
Bourbaki, N.: Elements of mathematics. Algebra. Chap. I–III. Paris: Hermann 1973
Cockcroft, A.M., Hudson, R.L.: Quantum mechanical Wiener processes. J. Multivariate Anal.7, 107–124 (1977)
Giri, N., von Waldenfels, W.: An algebraic version of the central limit theorem, Z. Wahrscheinlichkeitstheor. Verw. Geb.42, 129–134 (1978)
Hewitt, E., Ross, K.A.: Abstract harmonic analysis Vol. II. Die Grundlagen der mathematischen Wissenschaften Band 152. Berlin-Heidelberg-New York: Springer 1970
Heyer, H.: Probability measures on locally compact groups. Berlin-Heidelberg-New York: Springer 1977
Hudson, R.L., Lindsay, J.M.: Uses of non-Fock quantum Brownian motion and a quantum martingale representation theorem. Lect. Notes in Math. 1136. Berlin-Heidelberg-New York: Springer 1985
Hudson, R.L., Parthasarathy, K.R.: Quantum Ito's formula and stochastic evolutions. Commun. Math. Phys.93, 301–323 (1984)
Lang, S.: Algebra. Reading: Addison-Wesley 1971
Milnor, J.W., Moore, J.C.: On the structure of Hopf algebras. Ann. Math.81, 211–264 (1965)
von Neumann, J.: Collected works Vol. II. Einige Sätze über meßbare Abbildungen. Oxford: Pergamon Press 1961
Parthasarathy, K.R., Schmidt, K.: Positive definite kernels, continuous tensor products, and central limit theorems of probability theory. Lect. Notes in Math. 272. Berlin-Heidelberg-New York: Springer 1972
Schürmann, M.: Positive and conditionally positive linear functionals on coalgebras. Lect. Notes in Math. 1136. Berlin-Heidelberg-New York: Springer 1985
Schürmann, M.: Über *-Bialgebren und quantenstochastische Zuwachsprozesse. Dissertation, Heidelberg, 1985
Sweedler, M.E.: Hopf algebras. New York: Benjamin 1969
Takesaki, M.: Duality and von Neumann algebras. Lect. Notes in Math. 247. Berlin-Heidelberg-New York: Springer 1972
von Waldenfels, W.: An algebraic central limit theorem in the anti-commuting case. Z. Wahrscheinlichkeitstheor. Verw. Geb.42, 135–140 (1978)
von Waldenfels, W.: Ito solution of the linear quantum stochastic differential equation describing light emission and absorption. Lect. Notes in Math. 1055. Berlin-Heidelberg-New York: Springer 1984
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Accardi, L., Schürmann, M. & von Waldenfels, W. Quantum independent increment processes on superalgebras. Math Z 198, 451–477 (1988). https://doi.org/10.1007/BF01162868
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01162868