Dr Alexander Belton CMath, CSci, FIMA, SFHEA

Head of Department, Senior Lecturer in Pure Mathematics

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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.
Journal article

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.
Journal article

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.
Journal article

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.
Journal article

The convergence of unitary quantum random walks
Belton, A.C.R., Gnacik, M., Lindsay, J.M. 25/04/2014 , 13 p.
Working paper

Quantum random walks with general particle states
Belton, A.C.R. 16/02/2014 In: Communications in Mathematical Physics. 328, 2, p. 573-596. 24 p.
Journal article

Stopping the CCR flow and its isometric cocycles
Belton, A.C.R., Sinha, K.B. 5/02/2014 In: The Quarterly Journal of Mathematics. 65, 4, p. 1145-1164. 20 p.
Journal article

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.
Journal article

On stopping Fock-space processes
Belton, A.C.R. 20/11/2013 , 40 p.
Working paper

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.
Journal article

Quantum random walks and thermalisation
Belton, A.C.R. 12/2010 In: Communications in Mathematical Physics. 300, 2, p. 317-329. 13 p.
Journal article

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.
Journal article

Approximation via toy Fock space - the vacuum-adapted viewpoint
Belton, A.C.R. 09/2008 In: Quantum Stochastics and Information. Singapore : World Scientific p. 3-22. 20 p. ISBN: 978-981-283-295-5.
Chapter

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.
Journal article

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.
Journal article

Alicki-Fannes and Hudson-Parthasarathy evolution equations
Belton, A.C.R. 07/2007 In: Quantum Probability and Infinite Dimensional Analysis XX. Singapore : World Scientific p. 128-133. 6 p. ISBN: 978-981-270-851-9.
Chapter

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.
Journal article

The monotone Poisson process
Belton, A.C.R. 2006 In: Quantum Probability. Warsaw : Polish Academy of Sciences p. 99-115. 17 p.
Chapter

A note on vacuum-adapted semimartingales and monotone independence
Belton, A.C.R. 01/2005 In: Quantum Probability and Infinite Dimensional Analysis XVIII. Singapore : World Scientific p. 105-114. 10 p. ISBN: 978-981-256-147-3.
Chapter

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.
Journal article

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.
Journal article

A matrix formulation of quantum stochastic calculus
Belton, A.C.R. 1998 University of Oxford. 110 p.
Doctoral Thesis