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

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

 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 selfadjoint 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), 479501. View this article in WRRO
 Introductory topology, exercises and solutions by Mohammed Hichem Mortad, pp. 356, £40, (paper), ISBN 9789813148024, World Scientific (2017).. The Mathematical Gazette, 102(553), 185186. 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 Convolution semigroups of probability measures on Gelfand pairs, revisited. Communications on Stochastic Analysis, 10(4), 473490.
 The KalmanBucy filter for integrable Lévy processes with infinite second moment. Journal of Applied Probability, 52(03), 636648.
 The KalmanBucy filter for integrable Lévy processes with infinite second moment. Journal of Applied Probability, 52(3), 636648. 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), 15500031550003. View this article in WRRO
 Infinite dimensional OrnsteinUhlenbeck processes driven by Lévy processes. Probability Surveys, 12(0), 3354. 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 97809657063, ISBN 97809657070, Oxford Graduate Texts in Mathematics 24, Oxford University Press (2014).. The Mathematical Gazette, 98(543), 568570.
 Reviews  Concrete functional calculus, by R. M. Dudley and R. Norvaisa. Pp. 671, £90.00, 2011, ISSN 14397382, ISBN 9781441969491 (Springer Monographs in Mathematics).. The Mathematical Gazette, 98(541), 166168.
 Smoothness of densities on Compact Lie Groups. Rendiconti del Seminario Matematico, 71(2), 197208.
 View this article in WRRO A Generalised GangolliL evyKhintchine Formula for In nitely Divisible Measures and L evy Processes on SemiSimple Lie Groups and Symmetric Spaces. Annales d'Institut Henri Poincare: Probability and Statistics.
 Martingale transform and Levy processes on Lie groups. Indiana University Mathematics Journal.
 Introduction to the issue on differential geometry in signal processing. IEEE Journal on Selected Topics in Signal Processing, 7(4), 573575.
 Nonlinear Markov processes and kinetic equations (Cambridge Tracts in Mathematics 182). Bulletin of the London Mathematical Society, 43(6), 12451247.
 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 9781848825321 (Springer Monographs in Mathematics, SpringerVerlag London Ltd.). The Mathematical Gazette, 95(534), 571572.
 Pseudodifferential operators and Markov semigroups on compact Lie groups. Journal of Mathematical Analysis and Applications.
 STOCHASTIC STABILIZATION OF DYNAMICAL SYSTEMS USING LEVY NOISE. STOCH DYNAM, 10(4), 509527.
 Hilbert space methods and quantum mechanics, by Werner O. Amrein. Pp.395. $94.95 (hbk). 2009. ISBN: 978120066814 (CRC Press).. The Mathematical Gazette, 94(531), 571571.
 Probability measures on compact groups which have squareintegrable densities (vol 40, pg 1038, 2008). B LOND MATH SOC, 42, 948948.
 Advanced calculus: an introduction to linear analysis, by Leonard F. Richardson, J. Wiley and Sons, Inc. (2008), ISBN: 9780470232880 £78.50, $97.50 (hbk) pp.387.. The Mathematical Gazette, 94(530), 372373.
 Asymptotic Stability of Stochastic Differential Equations Driven by Lévy Noise. Journal of Applied Probability, 46(04), 11161129.
 View this article in WRRO ASYMPTOTIC STABILITY OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY LEVY NOISE. J APPL PROBAB, 46(4), 11161129.
 Extending stochastic resonance for neuron models to general Lévy noise.. IEEE Trans Neural Netw, 20(12), 19931995. View this article in WRRO
 Some L (2) properties of semigroups of measures on Lie groups. SEMIGROUP FORUM, 79(2), 217228. View this article in WRRO
 Probability measures on compact groups which have squareintegrable densities. B LOND MATH SOC, 40, 10381044. View this article in WRRO
 On the infinitesimal generators of OrnsteinUhlenbeck processes with jumps in Hilbert space. POTENTIAL ANAL, 26(1), 79100. View this article in WRRO
 A lévyciesielski expansion for quantum brownian motion and the construction of quantum brownian bridges. Journal of Applied Analysis, 13(2), 275290. View this article in WRRO
 View this article in WRRO Martingalevalued measures, OrnsteinUhlenbeck processes with jumps and operator selfdecomposability in Hilbert space. LECT NOTES MATH, 1874, 171196.
 Levy Processes in Euclidean Spaces and Groups. LECT NOTES MATH, 1865, 198.
 Levytype stochastic integrals with regularly varying tails. STOCH ANAL APPL, 23(3), 595611. 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 (SpringerVerlag).. The Mathematical Gazette, 88(512), 387388.
 Lévy processes  From probability to finance and quantum groups. Notices of the American Mathematical Society, 51(11), 13361347.
 On a class of nontranslation invariant Feller semigroups on Lie groups. POTENTIAL ANAL, 16(2), 103114.
 Stochastic flows of diffeomorpbisms on manifolds driven by infinitedimensional semimartingales with jumps. STOCH PROC APPL, 92(2), 219236.
 Operatorvalued stochastic differential equations arising from unitary group representations. J THEOR PROBAB, 14(1), 6176.
 Compound Poisson processes and Levy processes in groups and symmetric spaces. J THEOR PROBAB, 13(2), 383425.
 Stochastic partial differential equations driven by Levy spacetime white noise. Random Operators and Stochastic Equations, 8(3), 245259.
 Isotropic Levy processes on Riemannian manifolds. ANN PROBAB, 28(1), 166184.
 Invariant measures for Levy flows of diffeomorphisms. P ROY SOC EDINB A, 130, 925946.
 Quantum martingale measures and stochastic partial differential equations in Fock space. J MATH PHYS, 39(6), 30193030.
 Stochastic parallel transport along Levy flows of diffeomorphisms. J MATH ANAL APPL, 207(2), 496505.
 SPECTRAL FAMILIES OF QUANTUM STOCHASTIC INTEGRALS. COMMUN MATH PHYS, 170(3), 607628.
 FERMION STOCHASTIC CALCULUS IN DIRACFOCK SPACE. J PHYS AMATH GEN, 28(2), 257270.
 ON THE 2ND QUANTIZATION OF HILBERTSCHMIDT PROCESSES. ANN I H POINCAREPHY, 62(1), 116.
 UNITARY ACTIONS OF LEVY FLOWS OF DIFFEOMORPHISMS. J MULTIVARIATE ANAL, 49(2), 266277.
 LEVY FLOWS ON MANIFOLDS AND LEVY PROCESSES ON LIEGROUPS. J MATH KYOTO U, 33(4), 11031123.
 LEVY FLOWS ON MANIFOLDS AND OPERATORALGEBRAS. MATH NOTES+, 54(34), 981986.
 FERMIONIC STOCHASTIC DIFFERENTIALEQUATIONS AND THE INDEX OF FREDHOLM OPERATORS. LETT MATH PHYS, 28(3), 231237.
 Deformations of cocycles, quantum Lévy processes and quantum stochastic flows. Reports on Mathematical Physics, 32(1), 117132.
 On a class of stochastic flows driven by quantum Brownian motion. Journal of Theoretical Probability, 6(1), 1732.
 Brownian Motion on So(3) Factorises in Fock Space. Bulletin of the London Mathematical Society, 23(5), 493496.
 QUANTUM DIFFUSIONS ON INVOLUTIVE ALGEBRAS. LECTURE NOTES IN MATHEMATICS, 1442, 7085.
 Stochastic evolution of YangMills connections on the noncommutative twotorus. Letters in Mathematical Physics, 16(2), 9399.
 FERMION ITO FORMULA AND STOCHASTIC EVOLUTIONS. COMMUN MATH PHYS, 96(4), 473496.
 Aspects of Recurrence and Transience for Levy Processes in Transformation Groups and NonCompact Riemannian Symmetric Pairs.
 Infinitely divisible central probability measures on compact Lie groupsregularity, semigroups and transition kernels. Annals of Probability, 39(6), 24742496.
 Cylindrical Levy processes in Banach spaces.
Chapters
 Probability on Compact Lie Groups, International Encyclopedia of Statistical Science (pp. 11211123). Springer Berlin Heidelberg
 Lévy Processes in Stochastic Differential Geometry, Lévy Processes (pp. 111137). Birkhäuser Boston
 A horizontal levy process on the bundle of orthonormal frames over a complete Reimannian manifold, Lecture Notes in Mathematics (pp. 166180). Springer Berlin Heidelberg
 FERMION STOCHASTIC FLOWS ON QUANTUM ALGEBRAS, Quantum Probability and Related Topics (pp. 6787). WORLD SCIENTIFIC
Conference proceedings papers
 Stationary Random Fields on the Unitary Dual of a Compact Group. Séminaire de Probabilités XLVIII, Vol. 2168 (pp 469480) View this article in WRRO
 Probabilistic Approach to Fractional Integrals and the HardyLittlewoodSobolev Inequality. Analytic Methods in Interdisciplinary Applications, Vol. 116 (pp 1740). Switzerland, 5 August 2013  9 August 2013.
 Quantum diffusions on involutive algebras (pp 7085)
Working papers
 View this article in WRRO Pseudo Differential Operators and Markov Semigroups on Compact Lie Groups.
 View this article in WRRO Universal Malliavin Calculus in Fock and LévyItô Spaces.
 Research group
 Grants

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

Analysis, probability, measure theory