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Research

Professor Alexander Belton CMath, CSci, FIMA, SFHEA

Visiting Professor

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  1. 1998
  2. Published

    A matrix formulation of quantum stochastic calculus

    Belton, A. C. R., 1998, University of Oxford. 110 p.

    Research output: Thesis › Doctoral Thesis

  3. 2001
  4. Published

    Quantum Ω-semimartingales and stochastic evolutions

    Belton, A. C. R., 1/12/2001, In: Journal of Functional Analysis. 187, 1, p. 94-109 16 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  5. 2004
  6. Published

    An isomorphism of quantum semimartingale algebras

    Belton, A. C. R., 06/2004, In: The Quarterly Journal of Mathematics. 55, 2, p. 135-165 31 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  7. Published

    Erratum: An isomorphism of quantum semimartingale algebras (Quarterly Journal Mathematics (2004) 55 (135-165) DOI: 10.1093/qmath/hag052)

    Belton, A. C. R., 1/12/2004, In: Quarterly Journal of Mathematics. 55, 4, 1 p.

    Research output: Contribution to Journal/Magazine › Comment/debate › peer-review

  8. 2005
  9. Published

    A note on vacuum-adapted semimartingales and monotone independence

    Belton, A. C. R., 01/2005, Quantum Probability and Infinite Dimensional Analysis XVIII. Schuermann, M. & Franz, U. (eds.). Singapore: World Scientific, p. 105-114 10 p.

    Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter

  10. 2006
  11. Published

    The monotone Poisson process

    Belton, A. C. R., 2006, Quantum Probability. Bożejko, M., Młotkowski, W. & Wysoczański, J. (eds.). 73 ed. Warsaw: Polish Academy of Sciences, p. 99-115 17 p. (Banach Center Publications).

    Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter

  12. Published

    Some self-adjoint quantum semimartingales

    Belton, A. C. R., 1/05/2006, In: Proceedings of the London Mathematical Society. 92, 3, p. 791-816 26 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  13. 2007
  14. Published

    Alicki-Fannes and Hudson-Parthasarathy evolution equations

    Belton, A. C. R., 07/2007, Quantum Probability and Infinite Dimensional Analysis XX. Accardi, L., Freudenberg, W. & Schuermann, M. (eds.). Singapore: World Scientific, p. 128-133 6 p.

    Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter

  15. Published

    The chaotic-representation property for a class of normal martingales

    Belton, A. C. R. & Attal, S., 1/11/2007, In: Probability Theory and Related Fields. 139, 3-4, p. 543-562 20 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  16. 2008
  17. Published

    On the path structure of a semimartingale arising from monotone probability theory

    Belton, A. C. R., 2008, In: Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques. 44, 2, p. 258-279 22 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  18. Published

    Approximation via toy Fock space - the vacuum-adapted viewpoint

    Belton, A. C. R., 09/2008, Quantum Stochastics and Information. Belavkin, V. P. & Guţă, M. (eds.). Singapore: World Scientific, p. 3-22 20 p.

    Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter

  19. 2010
  20. Published

    Random-walk approximation to vacuum cocycles

    Belton, A. C. R., 04/2010, In: Journal of the London Mathematical Society. 81, 2, p. 412-434 23 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  21. Published

    Quantum random walks and thermalisation

    Belton, A. C. R., 12/2010, In: Communications in Mathematical Physics. 300, 2, p. 317-329 13 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  22. 2012
  23. Published

    A vacuum-adapted approach to quantum Feynman-Kac formulae

    Belton, A. C. R., Lindsay, J. M. & Skalski, A., 03/2012, In: Communications on Stochastic Analysis. 6, 1, p. 95-109 15 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  24. 2013
  25. Published

    On stopping Fock-space processes

    Belton, A. C. R., 20/11/2013, 40 p.

    Research output: Working paper

  26. 2014
  27. Published

    Quantum random walks with general particle states

    Belton, A. C. R., 2014, In: Communications in Mathematical Physics. 328, 2, p. 573-596 24 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  28. Published

    Stopping the CCR flow and its isometric cocycles

    Belton, A. C. R. & Sinha, K. B., 2014, In: The Quarterly Journal of Mathematics. 65, 4, p. 1145-1164 20 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  29. Published

    Quantum Feynman-Kac perturbations

    Belton, A. C. R., Lindsay, J. M. & Skalski, A. G., 02/2014, In: Journal of the London Mathematical Society. 89, 1, p. 275-300 26 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  30. Published

    The convergence of unitary quantum random walks

    Belton, A. C. R., Gnacik, M. & Lindsay, J. M., 25/04/2014, 13 p.

    Research output: Working paper

  31. 2015
  32. Published

    An algebraic construction of quantum flows with unbounded generators

    Belton, A. C. R. & Wills, S. J., 2015, In: Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques. 51, 1, p. 349-375 27 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  33. 2016
  34. Published

    Matrix positivity preservers in fixed dimension

    Belton, A., Guillot, D., Khare, A. & Putinar, M., 02/2016, In: Comptes Rendus Mathématique. 354, 2, p. 143-148 6 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  35. Published

    Schur polynomials and matrix positivity preservers

    Belton, A., Guillot, D., Khare, A. & Putinar, M., 25/05/2016, Proceedings of the 28th International Conference on Formal Power Series and Algebraic Combinatorics: FPSAC 2016 Vancouver, Canada. DMTCS Proceedings, p. 155-166 12 p.

    Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Conference contribution/Paper › peer-review

  36. Published

    Matrix positivity preservers in fixed dimension. I

    Belton, A., Guillot, D., Khare, A. & Putinar, M., 6/08/2016, In: Advances in Mathematics. 298, p. 325-368 44 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  37. Published

    Moment-sequence transforms

    Belton, A., Guillot, D., Khare, A. & Putinar, M., 27/10/2016, Arxiv, 33 p.

    Research output: Working paper

  38. 2017
  39. Published

    The cocycle identity holds under stopping

    Belton, A. C. R. & Sinha, K. B., 1/09/2017, In: The Quarterly Journal of Mathematics. 68, 3, p. 817-830 14 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

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