Professor David Applebaum

School of Mathematics and Statistics

Emeritus Professor

D.Applebaum@shef.ac.uk
+44 114 222 3703

Hicks Building

Full contact details

Professor David Applebaum
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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All publications

Books

Applebaum D (2014) Probability on Compact Lie Groups. Springer International Publishing.
Applebaum D (2008) Probability and Information. Cambridge University Press.

Journal articles

Applebaum D & Le Ngan T (2020) The positive maximum principle on symmetric spaces. Positivity. View this article in WRRO
Applebaum D & Brockway RS (2020) L2 properties of Lévy generators on compact Riemannian manifolds. Journal of Theoretical Probability. View this article in WRRO
Applebaum D & Le Ngan T (2019) The Positive Maximum Principle on Lie Groups. Journal of the London Mathematical Society. View this article in WRRO
Applebaum D (2019) On the spectrum of self-adjoint Lévy generators. Communications on Stochastic Analysis, 13(1). View this article in WRRO
Applebaum DB & Le Ngan T (2018) Transition Densities and Traces for Invariant Feller Processes on Compact Symmetric Spaces. Potential Analysis, 49(3), 479-501. View this article in WRRO
Applebaum D (2018) 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
Applebaum D (2017) Probabilistic trace and Poisson summation formulae on locally compact abelian groups. Forum Mathematicum, 29(6).
Applebaum D (2017) Probabilistic trace and Poisson summation formulae on locally compact abelian groups. Forum Mathematicum, 29(3). View this article in WRRO
Applebaum DB (2016) Convolution semigroups of probability measures on Gelfand pairs, revisited. Communications on Stochastic Analysis, 10(4), 473-490. View this article in WRRO
Applebaum D & Blackwood S (2015) The Kalman-Bucy filter for integrable Lévy processes with infinite second moment. Journal of Applied Probability, 52(03), 636-648.
Applebaum D & Blackwood S (2015) 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
Applebaum D & van Neerven J (2015) 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
Applebaum D (2015) Infinite dimensional Ornstein-Uhlenbeck processes driven by Lévy processes. Probability Surveys, 12(0), 33-54. View this article in WRRO
Applebaum D & van Neerven J (2014) Second quantisation for skew convolution products of measures in Banach spaces. Electronic Journal of Probability, 19. View this article in WRRO
Applebaum D (2014) 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.
Applebaum D (2014) 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.
Applebaum D (2013) Smoothness of densities on Compact Lie Groups. Rendiconti del Seminario Matematico, 71(2), 197-208.
Applebaum DB & Dooley A (2013) A Generalised Gangolli-L evy-Khintchine Formula for In nitely Divisible Measures and L evy Processes on Semi-Simple Lie Groups and Symmetric Spaces. Annales d'Institut Henri Poincare: Probability and Statistics. View this article in WRRO
Applebaum DB & Banuelos R (2013) Martingale transform and Levy processes on Lie groups. Indiana University Mathematics Journal.
Manton JH, Applebaum D, Ikeda S & Le Bihan N (2013) Introduction to the issue on differential geometry in signal processing. IEEE Journal on Selected Topics in Signal Processing, 7(4), 573-575.
Applebaum D (2011) Nonlinear Markov processes and kinetic equations (Cambridge Tracts in Mathematics 182). Bulletin of the London Mathematical Society, 43(6), 1245-1247.
Applebaum D (2011) 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.
Applebaum D (2011) Pseudo-differential operators and Markov semigroups on compact Lie groups. Journal of Mathematical Analysis and Applications.
Applebaum D & Siakalli M (2010) STOCHASTIC STABILIZATION OF DYNAMICAL SYSTEMS USING LEVY NOISE. STOCH DYNAM, 10(4), 509-527.
Applebaum D (2010) 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.
Applebaum D (2010) Probability measures on compact groups which have square-integrable densities (vol 40, pg 1038, 2008). B LOND MATH SOC, 42, 948-948.
Applebaum D (2010) 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.
Applebaum D & Siakalli M (2009) Asymptotic Stability of Stochastic Differential Equations Driven by Lévy Noise. Journal of Applied Probability, 46(04), 1116-1129.
Applebaum D & Siakalli M (2009) ASYMPTOTIC STABILITY OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY LEVY NOISE. J APPL PROBAB, 46(4), 1116-1129. View this article in WRRO
Applebaum D (2009) Extending stochastic resonance for neuron models to general Lévy noise.. IEEE Trans Neural Netw, 20(12), 1993-1995. View this article in WRRO
Applebaum D (2009) Some L (2) properties of semigroups of measures on Lie groups. SEMIGROUP FORUM, 79(2), 217-228. View this article in WRRO
Applebaum D (2008) Probability measures on compact groups which have square-integrable densities. B LOND MATH SOC, 40, 1038-1044. View this article in WRRO
Applebaum D (2007) On the infinitesimal generators of Ornstein-Uhlenbeck processes with jumps in Hilbert space. POTENTIAL ANAL, 26(1), 79-100. View this article in WRRO
Applebaum D (2007) 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
Applebaum D (2006) Martingale-valued measures, Ornstein-Uhlenbeck processes with jumps and operator self-decomposability in Hilbert space. LECT NOTES MATH, 1874, 171-196. View this article in WRRO
Applebaum D (2005) Levy Processes in Euclidean Spaces and Groups. LECT NOTES MATH, 1865, 1-98.
Applebaum D (2005) Levy-type stochastic integrals with regularly varying tails. STOCH ANAL APPL, 23(3), 595-611. View this article in WRRO
Applebaum D (2004) 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.
Applebaum D (2004) Lévy processes - From probability to finance and quantum groups. Notices of the American Mathematical Society, 51(11), 1336-1347.
Applebaum D (2002) On a class of non-translation invariant Feller semigroups on Lie groups. POTENTIAL ANAL, 16(2), 103-114.
Applebaum D & Tang FC (2001) Stochastic flows of diffeomorpbisms on manifolds driven by infinite-dimensional semimartingales with jumps. STOCH PROC APPL, 92(2), 219-236.
Applebaum D (2001) Operator-valued stochastic differential equations arising from unitary group representations. J THEOR PROBAB, 14(1), 61-76.
Applebaum D (2000) Compound Poisson processes and Levy processes in groups and symmetric spaces. J THEOR PROBAB, 13(2), 383-425.
Applebaum D & Wu JL (2000) Stochastic partial differential equations driven by Levy space-time white noise. Random Operators and Stochastic Equations, 8(3), 245-259.
Applebaum D & Estrade A (2000) Isotropic Levy processes on Riemannian manifolds. ANN PROBAB, 28(1), 166-184.
Applebaum D & Kunita H (2000) Invariant measures for Levy flows of diffeomorphisms. P ROY SOC EDINB A, 130, 925-946.
Applebaum D (1998) Quantum martingale measures and stochastic partial differential equations in Fock space. J MATH PHYS, 39(6), 3019-3030.
Applebaum D & Cohen S (1997) Stochastic parallel transport along Levy flows of diffeomorphisms. J MATH ANAL APPL, 207(2), 496-505.
APPLEBAUM D (1995) SPECTRAL FAMILIES OF QUANTUM STOCHASTIC INTEGRALS. COMMUN MATH PHYS, 170(3), 607-628.
APPLEBAUM D (1995) FERMION STOCHASTIC CALCULUS IN DIRAC-FOCK SPACE. J PHYS A-MATH GEN, 28(2), 257-270.
APPLEBAUM D (1995) ON THE 2ND QUANTIZATION OF HILBERT-SCHMIDT PROCESSES. ANN I H POINCARE-PHY, 62(1), 1-16.
APPLEBAUM D (1994) UNITARY ACTIONS OF LEVY FLOWS OF DIFFEOMORPHISMS. J MULTIVARIATE ANAL, 49(2), 266-277.
APPLEBAUM D & KUNITA H (1993) LEVY FLOWS ON MANIFOLDS AND LEVY PROCESSES ON LIE-GROUPS. J MATH KYOTO U, 33(4), 1103-1123.
APPLEBAUM D (1993) LEVY FLOWS ON MANIFOLDS AND OPERATOR-ALGEBRAS. MATH NOTES+, 54(3-4), 981-986.
APPLEBAUM D (1993) FERMIONIC STOCHASTIC DIFFERENTIAL-EQUATIONS AND THE INDEX OF FREDHOLM OPERATORS. LETT MATH PHYS, 28(3), 231-237.
Applebaum D (1993) Deformations of cocycles, quantum Lévy processes and quantum stochastic flows. Reports on Mathematical Physics, 32(1), 117-132.
Applebaum D (1993) On a class of stochastic flows driven by quantum Brownian motion. Journal of Theoretical Probability, 6(1), 17-32.
Applebaum D (1991) Brownian Motion on So(3) Factorises in Fock Space. Bulletin of the London Mathematical Society, 23(5), 493-496.
APPLEBAUM D (1990) QUANTUM DIFFUSIONS ON INVOLUTIVE ALGEBRAS. LECTURE NOTES IN MATHEMATICS, 1442, 70-85.
Applebaum D (1988) Stochastic evolution of Yang-Mills connections on the noncommutative two-torus. Letters in Mathematical Physics, 16(2), 93-99.
APPLEBAUM DB & HUDSON RL (1984) FERMION ITO FORMULA AND STOCHASTIC EVOLUTIONS. COMMUN MATH PHYS, 96(4), 473-496.
Applebaum D () Aspects of Recurrence and Transience for Levy Processes in Transformation Groups and Non-Compact Riemannian Symmetric Pairs.
Applebaum D () Infinitely divisible central probability measures on compact Lie groups---regularity, semigroups and transition kernels. Annals of Probability, 39(6), 2474-2496.
Applebaum D & Riedle M () Cylindrical Levy processes in Banach spaces.

Chapters

Applebaum D (2011) Probability on Compact Lie Groups, International Encyclopedia of Statistical Science (pp. 1121-1123). Springer Berlin Heidelberg
Applebaum D (2001) Lévy Processes in Stochastic Differential Geometry, Lévy Processes (pp. 111-137). Birkhäuser Boston
Applebaum D (1995) 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
Applebaum D (1994) FERMION STOCHASTIC FLOWS ON QUANTUM ALGEBRAS, Quantum Probability and Related Topics (pp. 67-87). WORLD SCIENTIFIC

Conference proceedings papers

Applebaum DB (2016) 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
Applebaum D & Bañuelos R (2015) 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.
Applebaum D (1990) Quantum diffusions on involutive algebras (pp 70-85)

Working papers

Applebaum D () Pseudo Differential Operators and Markov Semigroups on Compact Lie Groups. View this article in WRRO
Applebaum D () Universal Malliavin Calculus in Fock and Lévy-Itô Spaces. View this article in WRRO

Research group: Probability

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