Professor David Applebaum

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