Professor David Applebaum
School of Mathematics and Statistics
Emeritus Professor
+44 114 222 3703
Full contact details
School of Mathematics and Statistics
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
- Profile
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Professor Applebaum graduated with an MA from the University of St Andrews in 1979. He obtained an MSc in mathematical physics from Nottingham University (1982) and a PhD there in quantum probability (1984), supervised by R L Hudson. After postdoctoral appointments in Rome, Nottingham and Bielefeld, he took a lectureship at Nottingham Trent University (then Trent Polytechnic) in 1987, becoming a Reader in 1994 and Professor in 1998, before moving to Sheffield in 2004. Professor Applebaum now works in probability theory.
- Research interests
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- Stochastic calculus and stochastic differential equations driven by processes with jumps, especially Levy processes
- Probability theory on abstract structures - particularly Lie groups, symmetric spaces and Banach spaces
- Publications
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Books
- Probability on Compact Lie Groups. Springer International Publishing.
- Probability and Information. Cambridge University Press.
Journal articles
- The positive maximum principle on symmetric spaces. Positivity. View this article in WRRO
- L2 properties of Lévy generators on compact Riemannian manifolds. Journal of Theoretical Probability. View this article in WRRO
- The Positive Maximum Principle on Lie Groups. Journal of the London Mathematical Society. View this article in WRRO
- On the spectrum of self-adjoint Lévy generators. Communications on Stochastic Analysis, 13(1). View this article in WRRO
- Transition Densities and Traces for Invariant Feller Processes on Compact Symmetric Spaces. Potential Analysis, 49(3), 479-501. View this article in WRRO
- Introductory topology, exercises and solutions by Mohammed Hichem Mortad, pp. 356, £40, (paper), ISBN 978-9-81314-802-4, World Scientific (2017).. The Mathematical Gazette, 102(553), 185-186. View this article in WRRO
- Probabilistic trace and Poisson summation formulae on locally compact abelian groups. Forum Mathematicum, 29(6).
- Probabilistic trace and Poisson summation formulae on locally compact abelian groups. Forum Mathematicum, 29(3). View this article in WRRO
- View this article in WRRO
- The Kalman-Bucy filter for integrable Lévy processes with infinite second moment. Journal of Applied Probability, 52(03), 636-648.
- The Kalman-Bucy filter for integrable Lévy processes with infinite second moment. Journal of Applied Probability, 52(3), 636-648. View this article in WRRO
- Second quantisation for skew convolution products of infinitely divisible measures. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 18(01), 1550003-1550003. View this article in WRRO
- Infinite dimensional Ornstein-Uhlenbeck processes driven by Lévy processes. Probability Surveys, 12(0), 33-54. View this article in WRRO
- Second quantisation for skew convolution products of measures in Banach spaces. Electronic Journal of Probability, 19. View this article in WRRO
- Stochastic analysis and diffusion processes by G. Kallianpur and P. Sundar, pp 352, £65 (hbk), £29.99 (pbk) ISBN 978-0-965706-3, ISBN 978-0-965707-0, Oxford Graduate Texts in Mathematics 24, Oxford University Press (2014).. The Mathematical Gazette, 98(543), 568-570.
- Reviews -
Concrete functional calculus, by R. M. Dudley and R. Norvaisa. Pp. 671, £90.00, 2011, ISSN 1439-7382, ISBN 978-1-4419-6949-1 (Springer Monographs in Mathematics).. The Mathematical Gazette, 98(541), 166-168.
- View this article in WRRO
- Introduction to the issue on differential geometry in signal processing. IEEE Journal on Selected Topics in Signal Processing, 7(4), 573-575.
- Nonlinear Markov processes and kinetic equations
(Cambridge Tracts in Mathematics 182). Bulletin of the London Mathematical Society, 43(6), 1245-1247.
- Reviews -
Harmonic analysis of mean periodic functions on symmetric spaces and the Heisenberg group, by Valery V. Volchkov and Vitaly V. Volchkov. Pp. 671
$59. 99 (hbk). 2009. ISBN 978-1-84882-532-1 (Springer Monographs in Mathematics, Springer-Verlag London Ltd.). The Mathematical Gazette, 95(534), 571-572.
- STOCHASTIC STABILIZATION OF DYNAMICAL SYSTEMS USING LEVY NOISE. STOCH DYNAM, 10(4), 509-527.
- Hilbert space methods and quantum mechanics, by Werner O. Amrein. Pp.395. $94.95 (hbk). 2009. ISBN: 978-1-200-6681-4 (CRC Press).. The Mathematical Gazette, 94(531), 571-571.
- Probability measures on compact groups which have square-integrable densities (vol 40, pg 1038, 2008). B LOND MATH SOC, 42, 948-948.
- Advanced calculus: an introduction to linear analysis, by Leonard F. Richardson, J. Wiley and Sons, Inc. (2008), ISBN: 978-0-470-23288-0 £78.50, $97.50 (hbk) pp.387.. The Mathematical Gazette, 94(530), 372-373.
- Asymptotic Stability of Stochastic Differential Equations Driven by Lévy Noise. Journal of Applied Probability, 46(04), 1116-1129.
- View this article in WRRO
- Extending stochastic resonance for neuron models to general Lévy noise.. IEEE Trans Neural Netw, 20(12), 1993-1995. View this article in WRRO
- Some L (2) properties of semigroups of measures on Lie groups. SEMIGROUP FORUM, 79(2), 217-228. View this article in WRRO
- Probability measures on compact groups which have square-integrable densities. B LOND MATH SOC, 40, 1038-1044. View this article in WRRO
- On the infinitesimal generators of Ornstein-Uhlenbeck processes with jumps in Hilbert space. POTENTIAL ANAL, 26(1), 79-100. View this article in WRRO
- A lévy-ciesielski expansion for quantum brownian motion and the construction of quantum brownian bridges. Journal of Applied Analysis, 13(2), 275-290. View this article in WRRO
- View this article in WRRO
- Levy-type stochastic integrals with regularly varying tails. STOCH ANAL APPL, 23(3), 595-611. View this article in WRRO
- Elementary probability theory – with stochastic processes and an introduction to mathematical finance, (4th edn), by K. L. Chung and F. AitSahlia. Pp. 402. £56. 2003. ISBN 0 387 95578 X (Springer-Verlag).. The Mathematical Gazette, 88(512), 387-388.
- Stochastic partial differential equations driven by Levy space-time white noise. Random Operators and Stochastic Equations, 8(3), 245-259.
- Deformations of cocycles, quantum Lévy processes and quantum stochastic flows. Reports on Mathematical Physics, 32(1), 117-132.
- On a class of stochastic flows driven by quantum Brownian motion. Journal of Theoretical Probability, 6(1), 17-32.
- Brownian Motion on So(3) Factorises in Fock Space. Bulletin of the London Mathematical Society, 23(5), 493-496.
- Stochastic evolution of Yang-Mills connections on the noncommutative two-torus. Letters in Mathematical Physics, 16(2), 93-99.
- Infinitely divisible central probability measures on compact Lie
groups---regularity, semigroups and transition kernels. Annals of Probability, 39(6), 2474-2496.
- Cylindrical Levy processes in Banach spaces.
Chapters
- Probability on Compact Lie Groups, International Encyclopedia of Statistical Science (pp. 1121-1123). Springer Berlin Heidelberg
- Lévy Processes in Stochastic Differential Geometry, Lévy Processes (pp. 111-137). Birkhäuser Boston
- A horizontal levy process on the bundle of orthonormal frames over a complete Reimannian manifold, Lecture Notes in Mathematics (pp. 166-180). Springer Berlin Heidelberg
- FERMION STOCHASTIC FLOWS ON QUANTUM ALGEBRAS, Quantum Probability and Related Topics (pp. 67-87). WORLD SCIENTIFIC
Conference proceedings papers
- Stationary Random Fields on the Unitary Dual of a Compact Group. Séminaire de Probabilités XLVIII, Vol. 2168 (pp 469-480) View this article in WRRO
- Probabilistic Approach to Fractional Integrals and the Hardy-Littlewood-Sobolev Inequality. Analytic Methods in Interdisciplinary Applications, Vol. 116 (pp 17-40). Switzerland, 5 August 2013 - 9 August 2013.
- Quantum diffusions on involutive algebras (pp 70-85)
Working papers
- View this article in WRRO
- View this article in WRRO
- Probability on Compact Lie Groups. Springer International Publishing.
- Research group
- Grants
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Past grants, as Principal Investigator
Probability - Theory and applications (workshop) EPSRC Probability - Theory and applications (workshop) EPSRC Past grants, as Coinvestigator
Noncommutativity, geometry and probability EPSRC
- Teaching interests
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Analysis, probability, measure theory