Quantum martingales and stochastic integrals

  • Ivan F. Wilde
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1303)


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  1. 1.
    Applebaum, D.B., Hudson, R.L.: Fermion Itô's formula and stochastic evolutions. Commun. Math. Phys. 96, 473–496 (1984).CrossRefMATHGoogle Scholar
  2. 2.
    Barnett, C., Streater, R.F., Wilde, I.F.: The Itô-Clifford integral. J. Funct. Anal. 48, 172–212 (1982).MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Barnett, C., Streater, R.F., Wilde, I.F.: Quasi-free quantum stochastic integrals for the CAR and CCR. J. Funct. Anal. 52, 19–47 (1983).MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Barnett, C., Wilde, I.F.: Natural processes and Doob-Meyer decompositions over a probability gage space. J. Funct. Anal. 58, 320–334 (1984).MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Barnett, C., Wilde, I.F.: The Doob-Meyer decomposition for the square of Itô-Clifford L2-martingales. In Quantum probability and applications II, Lecture Notes in Mathematics 1136, Eds. Accardi, L., von Waldenfels, W., Springer-Verlag 1985.Google Scholar
  6. 6.
    Barnett, C., Wilde, I.F.: Belated integrals. J. Funct. Anal. 66, 283–307 (1986).MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Cairoli, R., Walsh, J.B.: Stochastic integrals in the plane. Acta Math. 134, 111–183 (1975).MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Hudson, R.L., Lindsay, J.M.: A non-commutative martingale representation theorem for non-Fock quantum Brownian motion. J. Funct. Anal. 61, 202–221 (1985).MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Hudson, R.L., Lindsay, J.M., Parthasarathy, K.R.: Stochastic integral representation of some quantum martingales in Fock space. In Proc. of Symp. on Stoch. D.E. and Appl. (Warwick 1985), Ed. Elworthy, K.D. Pitman Lecture Note Series.Google Scholar
  10. 10.
    Hudson, R.L., Parthasarathy, K.R.: Quantum Itô's formula and stochastic evolutions. Commun. Math. Phys. 93, 301–323 (1984).MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Journé, J-L., Meyer, P.A.: In Séminaire Probabilité XX, Lecture Notes in Mathematics 1204, Eds. Aźema, J., Yor, M., Springer-Verlag 1986.Google Scholar
  12. 12.
    Lindsay, J.M.: Fermion martingales. Probab. Th. Rel. Fields 71, 307–320 (1986).MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Lindsay, J.M., Wilde, I.F.: On non-Fock boson stochastic integrals. J. Funct. Anal. 65, 76–82 (1986).MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Parthasarathy, K.R., Sinha, K.B.: Stochastic integral representation of bounded quantum martingales in Fock spaces. J. Funct. Anal. 67, 126–151 (1986).MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Segal, I.E.: A non-commutative extension of abstract integration. Ann. of Math. 57, 401–457 (1953).MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Walsh, J.B.: Martingales with a multidimensional parameter and stochastic integrals in the plane. In Lectures in probability and statistics, Lecture Notes in Mathematics 1215, Eds. del Pino, G., Rebolledo, R., Springer-Verlag 1986.Google Scholar
  17. 17.
    Wong, E., Zakai, M.: Martingales and stochastic integrals for processes with a multi-dimensional parameter. Z. Warsch. verw. Gebiete 29, 109–122 (1974).MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Yeadon, F.J.: Non-commutative LP-spaces. Math. Proc. Cabm. Phil. Soc. 77, 91–102 (1975).MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Ivan F. Wilde
    • 1
  1. 1.Department of MathematicsKing's College StrandLondon

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