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Quantum independent increment processes on superalgebras

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References

  1. Abe, E.: Hopf algebras. Cambridge: University Press 1980

    Google Scholar 

  2. Accardi, L.: Non-relativistic quantum mechanics as a non-commutative Markov process. Adv. Math.20, 329–366 (1976)

    Google Scholar 

  3. Accardi, L., Parthasarathy, K.R.: A martingale characterisation of canonical commutation and anticommutation relations, submitted for publication

  4. Accardi, L., Frigerio, A., Lewis, J.T.: Quantum stochastic processes. Publ. RIMS, Kyoto Univ.18, 97–133 (1982)

    Google Scholar 

  5. Applebaum, D.: The strong Markov property for Fermion Brownian motion. J. Funct. Anal.65, 273–291 (1986)

    Google Scholar 

  6. Applebaum, D., Hudson, R.L.: Fermion Ito's formula and stochastic evolutions. Commun. Math. Phys.96, 473–496 (1984)

    Google Scholar 

  7. Bourbaki, N.: Eléments de mathématique. Théorie des ensembles. Paris: Hermann 1970

    Google Scholar 

  8. Bourbaki, N.: Elements of mathematics. Algebra. Chap. I–III. Paris: Hermann 1973

    Google Scholar 

  9. Cockcroft, A.M., Hudson, R.L.: Quantum mechanical Wiener processes. J. Multivariate Anal.7, 107–124 (1977)

    Google Scholar 

  10. Giri, N., von Waldenfels, W.: An algebraic version of the central limit theorem, Z. Wahrscheinlichkeitstheor. Verw. Geb.42, 129–134 (1978)

    Google Scholar 

  11. Hewitt, E., Ross, K.A.: Abstract harmonic analysis Vol. II. Die Grundlagen der mathematischen Wissenschaften Band 152. Berlin-Heidelberg-New York: Springer 1970

    Google Scholar 

  12. Heyer, H.: Probability measures on locally compact groups. Berlin-Heidelberg-New York: Springer 1977

    Google Scholar 

  13. 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

    Google Scholar 

  14. Hudson, R.L., Parthasarathy, K.R.: Quantum Ito's formula and stochastic evolutions. Commun. Math. Phys.93, 301–323 (1984)

    Google Scholar 

  15. Lang, S.: Algebra. Reading: Addison-Wesley 1971

    Google Scholar 

  16. Milnor, J.W., Moore, J.C.: On the structure of Hopf algebras. Ann. Math.81, 211–264 (1965)

    Google Scholar 

  17. von Neumann, J.: Collected works Vol. II. Einige Sätze über meßbare Abbildungen. Oxford: Pergamon Press 1961

    Google Scholar 

  18. 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

    Google Scholar 

  19. Schürmann, M.: Positive and conditionally positive linear functionals on coalgebras. Lect. Notes in Math. 1136. Berlin-Heidelberg-New York: Springer 1985

    Google Scholar 

  20. Schürmann, M.: Über *-Bialgebren und quantenstochastische Zuwachsprozesse. Dissertation, Heidelberg, 1985

  21. Sweedler, M.E.: Hopf algebras. New York: Benjamin 1969

    Google Scholar 

  22. Takesaki, M.: Duality and von Neumann algebras. Lect. Notes in Math. 247. Berlin-Heidelberg-New York: Springer 1972

    Google Scholar 

  23. von Waldenfels, W.: An algebraic central limit theorem in the anti-commuting case. Z. Wahrscheinlichkeitstheor. Verw. Geb.42, 135–140 (1978)

    Google Scholar 

  24. 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

    Google Scholar 

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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

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