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PUBLICATIONS OF D.APPLEBAUM
(I) BOOKS :
1)
D.Applebaum, Probability and Information, an Integrated Approach,
Cambridge University Press (1996), second edition (2008)
2)
D.Applebaum, Levy Processes and Stochastic Calculus, Cambridge University
Press (2004), second edition (2009)
3)
D.Applebaum, Limits, Limits Everywhere, Oxford University Press (2012)
4)
D.Applebaum, Probability on Compact Lie Groups, Springer (2014)
(II) RESEARCH PAPERS
1) D.Applebaum, R.L.Hudson, Fermion Diffusions, Journal of Mathematical
Physics, 25, 851-61 (1984)
2) D.Applebaum, R.L.Hudson, Fermion Ito's formula and stochastic evolutions,
Communications in Mathematical Physics 96, 473-96 (1984)
3) D.Applebaum, Quasi-free stochastic evolutions, in Springer Lecture Notes in
Mathematics 1136, 46-57 (1985)
4) D.Applebaum, The strong Markov property for Fermion Brownian motion,
Journal of Functional Analysis 65, 273-91 (1986),
5) D.Applebaum, Stochastic dilations of the Bloch equations in Boson and
Fermion noise, Journal of Physics A: Math. Gen. 19, 937-59 (1986),
6) D.Applebaum, A.Frigerio, Stationary dilations of W*-dynamical systems
constructed via stochastic differential equations, in Pitman Research
Notes in Mathematics 150, 1-38 (1987),
7) D.Applebaum, P.Robinson, Stochastic evolution of a harmonic oscillator in a
photon reservoir, Journal of Physics A: Math. Gen. 20, 1787-94 (1987),
8) D.Applebaum, Fermion Ito's formula II: The gauge process in Fermion Fock
space, Publications of the Research Institute of Mathematical
Sciences (Kyoto) 23, 17-56 (1987)
9) D.Applebaum, The stochastic Wigner-Wiesskopf atom, Journal of Mathematical
Physics 28 ,1858-64 (1987),
10) D.Applebaum, Quantum stochastic parallel transport on non-commutative
vector bundles, in Springer Lecture Notes in Mathematics 1303, 20-37
(1988)
11) D.Applebaum, Stochastic evolution of Yang-Mills connections on the
non-commutative two-torus, Letters in Mathematical Physics 16, 93-99
(1988)
12) D.Applebaum, Stopping unitary processes in Fock space, Publications of the
Research Institute of Mathematical Sciences (Kyoto) 24, 697-705 (1988)
13) D.Applebaum, Quantum diffusions on involutive algebras, in
Springer Lecture Notes in Mathematics 1442, 70-86 (1990)
14) D.Applebaum, Towards a quantum theory of classical diffusions on
Riemannian manifolds , in Quantum Probability and Related Topics VI, 93111 (1991)
15) D.Applebaum, Unitary evolutions and horizontal lifts in quantum
stochastic calculus, Communications in Mathematical Physics 140, 63-80
(1991)
16) D.Applebaum, Brownian motion on SO(3) factorises in Fock space,
Bulletin of the London Mathematical Society 23, 493-6 (1991)
17) D.Applebaum, An operator theoretic approach to stochastic flows on
manifolds, Seminaire de Probabilites XXVI, 514 - 33 (1992)
18) D.Applebaum, On a class of stochastic flows driven by quantum Brownian
motion, Journal of Theoretical Probability 6, 17-32 (1993)
19) D.Applebaum, Fermionic stochastic differential equations and the index of
Fredholm operators, Letters in Mathematical Physics, 28, 231 - 7 (1993)
20) D.Applebaum, Deformations of cocycles, quantum Levy processes and quantum
stochastic flows, Reports on Mathematical Physics 32, 117-32 (1993),
21) D.Applebaum, Quantum stochastic flows on manifolds I,
Quantum Probability and Related Topics VIII, 19-37 (1993)
22) D.Applebaum, H.Kunita, Levy flows on manifolds and Levy processes on Lie
groups, Journal of Mathematics of Kyoto University 33, 1103-23 (1993),
23) D.Applebaum, Levy flows on manifolds and operator algebras,
Matematicheskie Zametki 54, 3-11 (1993), Eng trans - Mathematical Notes
54, 981-6 (1993)
24) D.Applebaum, Unitary actions of Levy flows of diffeomorphisms, Journal of
Multivariate Analysis 49, 266-77 (1994),
25) D.Applebaum, Fermion stochastic flows on quantum algebras, Quantum
Probability and Related Topics IX, 67-89 (1994)
26) D.Applebaum, Spectral families of quantum stochastic integrals,
Communications in Mathematical Physics 170, 607-28 (1995)
27) D.Applebaum, Fermion stochastic calculus in Dirac Fock space, Journal of
Physics A: Math.Gen 28, 257-70 (1995),
28) D.Applebaum, On the second quantisation of Hilbert-Schmidt processes,
Annales d'Institute Henri Poincare (Phys Theor) 62, 1-16 (1995)
29) D.Applebaum, A horizontal Levy process on the bundle of orthonormal frames
over a Riemannian manifold, Seminaire de Probabilites XXIX, 166-81
(1995)
30) D.Applebaum, Covariant Poisson fields in Fock space, in
"Analysis, Geometry and Probability, Essays in Honour of
K.R.Parthasarathy", ed. R.Bhatia, Hindustan Book Agency,
1-16 (1996)
31) D.Applebaum, M.J.Brooks, Infinite series of quantum spectral stochastic
integrals, Journal of Operator Theory, 36, 295-316 (1996)
32) D.Applebaum, S.Cohen, Stochastic parallel transport along Levy flows of
diffeomorphisms, Journal of Mathematical Analysis and Applications, 207,
1496-505 (1997),
33) D.Applebaum, Quantum martingale measures and stochastic partial
differential equations in Fock space, Journal of Mathematical Physics
39, 3019-30 (1998)
34) D.Applebaum, Compound Poisson processes and Levy processes in groups
and symmetric spaces, Journal of Theoretical Probability 13, 383-425 (2000)
35) D.Applebaum, A.Estrade, Isotropic Levy processes on Riemannian manifolds,
Annals of Probability 28, 166-84 (2000)
36) D.Applebaum, H.Kunita, Invariant measures for Levy flows of
diffeomorphisms, Proceedings of the Royal Society of Edinburgh
(Mathematics) 130A, 1-22 (2000)
37) D.Applebaum, J.L.Wu, Stochastic partial differential equations
driven by Levy space-time white noise, Random Operators and
Stochastic Equations 8, 245-60 (2000)
38) D.Applebaum, Levy processes in stochastic differential geometry,
"Levy Processes: Theory and Applications", Birkhauser , 111-39 (2001)
39) D.Applebaum, Operator-valued stochastic differential equations arising
from unitary group representations, Journal of Theoretical
Probability 14, 61-76 (2001)
40) D.Applebaum, F.Tang, Stochastic flows of diffeomorphisms on manifolds
driven by infinite dimensional semimartingales with jumps, Stochastic
Processes and their Applications 92, 219-36 (2001)
41) D.Applebaum, F.Tang, The interlacing construction for stochastic flows
of diffeomorphisms on Euclidean spaces , Sankhya, Series A 63, 139-78 (2001)
42) D.Applebaum, On a class of non-translation invariant Feller semigroups on
Lie groups, Potential Analysis 16, 103-14 (2002)
43) D.Applebaum, On the subordination of spherically symmetric Levy processes
in Lie groups, International Mathematical Journal 1, 185-95 (2002)
44) D.Applebaum, Levy-type stochastic integrals with heavy
tails in Proceedings of the 2nd international workshop in
Applied Probability 40-4 (2004)
45) D.Applebaum, S.Cohen, Pseudodifferential operators, Levy
processes and Dirichlet forms in the Heisenberg group,
Annales de la Faculte des Sciences de Toulouse 13, 149-77
(2004)
46) D.Applebaum, Levy processes in Euclidean spaces and groups
in Quantum Independent Increment Processes I: From Classical
Probability to Quantum Stochastic Calculus, Springer Lecture Notes
in Mathematics}, Vol. 1865 M Schurmann, U. Franz (Eds.)
1-99(2005)
47) D.Applebaum, Levy-type stochastic integrals with regularly
varying tails, Stochastic Analysis and its Applications, 23, 1-18 (2005)
48) D.Applebaum, Martingale-valued measures, Ornstein-Uhlenbeck
processes with jumps and operator self-decomposability in Hilbert
space, Seminaire de Probabilites 39, 171-96 (2006)
49) D.Applebaum, Brownian motion and Levy processes on locally
compact groups, Methods of Functional Analysis and Topology
12, 101-112 (2006)
50) D.Applebaum, Covariant Mehler semigroups in Hilbert space,
Markov Processes and Related Fields 13, 159-69 (2007)
51) D.Applebaum, On the infinitesimal generators of Ornstein-Uhlenbeck processes
with jumps in Hilbert Space, Potential Analysis 26, 79-100 (2007)
52) D.Applebaum, Levy processes and stochastic integrals in
Banach spaces, Probability and Mathematical Statistics 27, 75-88 (2007)
53) D.Applebaum, A Levy-Ciesielski expansion for quantum
Brownian motion and the construction of quantum Brownian bridges,
Journal of Applied Analysis 13, 275-90 (2007)
54) D. Applebaum, Probability measures on compact groups which have squareintegrable densities, Bulletin of the London Math Soc. 40 1038-44 (2008),
Corrigendum 42 948 (2010)
55) D.Applebaum, Universal Malliavin calculus in Fock and Levy-Ito spaces,
Communications on Stochastic Analysis 3 119-41 (2009)
56) D.Applebaum, Some $L^{2}$ properties of semigroups of measures on Lie
groups, Semigroup Forum, 79 217-28 (2009)
57) D.Applebaum, M.Siakalli, Asymptotic stability of stochastic differential
equations driven by Levy processes, Journal of Applied Probability 46 111629 (2009)
58) D.Applebaum, Extending stochastic resonance for neuron models to general
Levy noise, IEEE Transactions on Neural Networks 20 1993-6 (2009)
59) D.Applebaum, M.Siakalli Stochastic stabilization of dynamical systems using
Levy noise, Stochastics and Dynamics 10 509-27 (2010)
60) D.Applebaum, M.Riedle, Cylindrical Levy processes in Banach spaces.
Proceedings of the London Math. Soc. 101 697-726 (2010)
61) D.Applebaum, Probability on compact Lie groups, International
Encyclopedia of Statistical Sciences (Springer) ed. M.Liodrag, 1121-23
(2011)
62) D.Applebaum, Infinitely divisible central probability measures on compact
Lie groups - regularity, semigroups and transition kernels, Annals of
Probability, 39 2474-96 (2011)
63) D.Applebaum, Pseudo differential operators and Markov semigroups on
compact Lie groups, Journal of Mathematical Analysis and Applications, 384,
331-48 (2011)
64) D.Applebaum, Aspects of recurrence and transience for Levy processes in
transformation groups and non-compact Riemannian symmetric pairs,
Journal of the Australian Math. Soc. 94, 304-20 (2013)
65) D.Applebaum, J. Van Neerven, Second quantisation for skew convolution
products of measures in Banach spaces, Electronic Journal of Probability 19,
paper 11 (17 pages)
66) D.Applebaum, Smoothness of densities on compact Lie groups, to appear in
Rendiconti del Seminario Matematico
67) D.Applebaum, R.Banuleos, Martingale transform and Levy processes on Lie
Groups, to appear in Indiana University Math Journal
68) D.Applebaum, A .Dooley, A Generalised Gangolli-Levy-Khintchine formula
for infinitely divisible measures and Levy processes on semi-simple Lie groups
and symmetric spaces, to appear in Annales Institut Henri Poincare (Prob.Stat.)
69) D.Applebaum, R.Banuleos, Probabilistic approach to fractional integrals and
the Hardy-Littlewood-Sobolev inequality, to appear in Proceedings of 9th
Isaac Congress (Springer)
70) D.Applebaum, S.Blackwood, The Kalman-Bucy filter for integrable Levy
processes with infinite second moment, to appear in Journal of Applied
Probability
71) D.Applebaum, J. van Neerven, Second quantisation for skew convolution
products of infinitely divisible measures, to appear in Infinite Dimensional
Analysis and Quantum Probability
(III) General Papers
72) D.Applebaum, Dirac operators - from differential calculus to the index
theorem, The Mathematical Scientist 25, 63-71 (2000)
73) D.Applebaum, Levy processes - from probability theory to
finance and quantum groups, Notices of the American Math
Soc. 51, 1336-47 (2004)
74) D.Applebaum, Robin Hudson's pathless path to quantum stochastic calculus,
Communications on Stochastic Analysis 4, 481-91 (2010)
75) D.Applebaum, extended book review of V.Kolokoltsov, "Nonlinear Markov
Processes and Kinetic Equations", Bull. London Math. Soc. 43, 1245–1249
(2011)