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FORSCHUNGSBERICHT 1999-2001

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Institut für Angewandte Mathematik Abt.f.Wahrsch.theorie u.Math.Statistik

Allgemeine Angaben:
Wegelerstraße 6, 53115 Bonn
Telefon: 0228 / 73-3417
Fax: 0228 / 73-9537
WWW: http://www-wt.iam.uni-bonn.de/

Hauptamtliche Professoren:
Prof. Dr. Sergio Albeverio
Prof. Dr. Yuri Kondratiev
Prof. Dr. Manfred Schäl
Prof. Dr. Karl-Theodor Sturm

Wissenschaftliches Personal:
Universitätsstellen
Dipl. Math. Giuliana Betro
Dr. Atle Hahn
Dipl. Math. Matthias Horst
Dr. Volker Jentsch
Dr. Lanjun Lao
Dr. Song Liang
Dr. Eugene Lytvynov
Dipl. Math. Steffan Alexe Popovici
Dr. Barbara Rüdiger
Dipl. Math. Michael Schmitz

Drittmittelstellen
Prof. Dr. Yana Belopolskaya
Prof. Dr. Yuri Berezansky
Dr. Maria Simonetta Bernabei
Dr. Zdzislaw Brzezniak
Dipl. Math. Tom Christiansen
Dr. Alexei Daletskii (DFG)
Dr. Shao Ming Fei (DFG)
Dr. Benedetta Ferrario
Prof. Gerald Goldin (A.v.H.)
Dr. Hanno Gottschalk
Dr. Martin Grothaus (SFB)
Dipl. Math. Martin Hesse
Dr. Tobias Kuna (GK)
Prof. Dr Lakaev
Dr. Lanjun Lao (WHK)
Dr. Xue Mei Li (A.v.H.)
Dr. Maria Joao Oliveira
Dr. Gustav Paulik
Prof. Dr. Sylvie Paycha (A.v.H.)
Dr. Barbara Rüdiger
Prof. Dr. Ambar Sengupta (A.v.H.)
Dr. Victoria Steblovskaja (A.v.H.)
Dipl. Phys. Horst Thaler (Österreich, BMW)
PD. Dr. Anton Thalmaier (DFG)
Dr. Max-Konstantin v. Renesse (SFB)
Dr. Jang-Lung Wu (DFG)
Dr. Xue Lei Zhao (A.v.H.)

Stipendiaten
P. Giordano
M. J. Oliveira

Forschungsschwerpunkte:
Mathematisches Modellieren im Bereich Finanzmathematik und Biologie
(Albeverio, Betro, Horst, Kondratiev, Lao, Popovici, Steblovskaja, Zhao)

Zufallsfelder und Statistische Physik
(Albeverio, Daletskii, Kondratiev, Kuna, Lytvynov)

Geometrische Stochastische Analysis
(Albeverio, Daletski, Li, Sturm, Thaler, Thalmaier)

Mathematische Physik : Quantentheorie, Quantenfeldtheorie,Chaostheorie, Hydrodynamik
(Albeverio, Fei, Ferrario, Gottschalk, Grothaus, Hahn, Kondratiev, Sengupta)

Unendlichdimensionale Analysis
(Albeverio, Grothaus, Hahn, Kondratiev, Liang, Paycha, Sengupta)

Theorie und Anwendung stochastischer Prozeße auf diskrete Strukturen
(Albeverio, Hesse, Sturm, Yasuda, Zhao)

Komplexe Systeme
(Albeverio, Jentsch, Kondratiev, Bogomolski, Giordano)

Dirichlet-Formen und Markov-Prozesse
(Albeverio, Kondratiev, Paulik, v. Renesse, Rüdiger, Sturm, Wu)

Funktionalanalysis, Halbgruppentheorie
(Albeverio, Kondratiev, Sturm)

Stochastik der Finanzmärkte : Stochastische Analysis von Optionen, Martingalmethoden
(Albeverio, Lao, Schäl, Steblovskaja, Zhao)

Stochastische Analysis
(Albeverio, Li, Schäl, Steblovskaja, Sturm)

Nonstandard Analysis und deren Anwendungen
(Albeverio, Wu)

Kontrolle Stochastischer Prozesse : Dynamische Optimierung, Markoff-Modelle
(Schäl, Schmitz)

Besondere Forschungsförderung:
436 RUS 113/534

Projekt zum Thema "Evolution processes in nonhomogeneous and random media"
(Bogachev, Kozlov, DFG)

436 RUS 113/570

Projekt zum Thema "Structure of the scattering matrix and resolvent on unphysical energy sheets and resonances in three-body quantum systems"
(Motovilov, Agaverdiev, DFG)

436 RUS 113/593

Projekt zum Thema "Stochastic processes and measures associated with nonlinear problems of mathematical and statistical physics
(Belopolskaya, Shelkovich, Smorodina, Feller, Pechersky, DFG)

436 UKR 113/39

Projekt zum Thema "Infinite dimensional analysis. In particular, generalized functions of infinitely many variables. Theory and applications
(Berezansky, Mierzejewski, DFG)

436 UKR 113/43

Deutsch-Ukrainische Zusammenarbeit zum Thema "Theory of singular perturbations.Schrödinger operators with point-like interactions and fractal potentials
(Koshmanenko, Konstantinov, DFG)

436 UKR 113/53

Projekt zum Thema "Singular probability via fractal approach and their applications"
(Korolyuk, Pratsiovytyi, Konstantinov, Torbin, DFG)

436 USB 113/3

Deutsch-Usbekische Zusammenarbeit zum Thema "Spectral analysis of three and four particle Schrödinger operators on a lattice"
(Lakaev, Muminov, Abdullaev, Shermatov, DFG)

INTAS projekt 94-2763

"Asymptotic methods in theoretical and mathematical physics"
(Maslov, Kolokoltsov, INTAS)

INTAS projekt 94-2763

"Asymptotic methods in theoretical and mathematical physics"
(Maslov, Kolokoltsov, INTAS)

Mitarbeit im DFG-Schwerpunktbereich "Interagierende stochastische Systeme von hoher Komplexität"
(Albeverio, Sturm, DFG)

Mitarbeit im SFB 256, Projekt B1 "Elliptische Systeme und Stochastische Analysis"
(Albeverio, Sturm, SFB)

Mitarbeit in SFB 257
(Albeverio)

Projekt-Nr:UKR 99/004

"Spektren und Zustände von Hamilton-Operatoren der Supraleitfähigkeit und Suprafluidität"
(Petrina, Rebenko, Finkelshtein, Deutsches Zentrum für Luft- und Raumfahrt e.V.(DLR))

Veröffentlichungen:

Albeverio S, Bayod L M, Perez-Garsia C, Cianci R, Khrennikov A
Non-Archimedean analogues of orthogonal and symmetric operators and p-adic quantization
Acta Appl. Math. 57, 205-237 (1999)

Albeverio S, Bogachev L V, Molchanov S A, Yarovaya E B
Annealed moment Lyapunov exponents for a branching random walk in a homogeneous random branching environment
Markov Process. Related Fields 6, no. 4, 473-516 (2000)

Albeverio S, Bogachev V, Röckner R
On uniqueness of invariant measures for finite and infinite dimensional diffusions
Comm. Pure Appl. Math. 52, 325-362 (1999)

Albeverio S, Chalimourda A, Podlaha O G
Non linear system analysis of a 87 Sr | 86 Sr time series for phanerozoic seawater
Chem. Geology 161, 241-252 (1999) (Special Issue: Earth System Evolution: Geochemical perspective, Ed. L. Veizer)

Albeverio S, Cianci R, De Grande-De Kimpe N, Khrennikov A
P-adic probability, and interpretation of negative probabilities in quantum mechanics
Russ. J. Math. Phys. 6, No 1, 3-19 (1999) (russ.) (transl. Oct. 1999)

Albeverio S, Daletskii A
Stochastic equations and quasi-invariance on infinite product groups
Inf. Dim. Anal. Quant. Prob. 2, 282-288 (1999)

Albeverio S, Daletskii A
Quasi-invariance and Gibbs structure of diffusion measures on infinite product groups
Methods Funct. Anal. Topology 6, no.1, 28-42 (2000)

Albeverio S, Daletskii A, Kondratiev Y
Stochastic analysis on infinite dimensional product manifolds
pp. 339-370 in ``Stochastic Dynamics'', Eds. H. Crauel, M. Gundlach (Dedicated to L. Arnold), Springer (1999)

Albeverio S, Daletskii A, Kondratiev Y
Stochastic analysis on product manifolds: Dirichlet operators on differential forms
J. Funct. Anal. 176, no. 2, 280-316 (2000)

Albeverio S, Daletskii A, Kondratiev Y, Röckner M
Fluctuations and their Glauber dynamics in lattice systems
J. Funct. Anal. 166, 148-167 (1999)

Albeverio S, Daletskii A, Lytvynov E
Laplace operators on differential forms over configuration spaces
J. Geom. Phys. 37, no.1-2, 15-46 (2000)

Albeverio S, Daletskii A, Lytvynov E
Laplace operators and diffusions in tangent bundles over Poisson spaces
pp. 1-25 in Ph. Clement, F. den Hollander, J. van Neeven, B. de Pagter, eds., Infinite Dimensional Stochastic Analysis, Roy. Neth. Acad. Arts & Science, Amsterdam (2000)

Albeverio S, Daletskii A, Lytvynov E
Stochastic Dynamics of compact spins: ergodicity and irreducibility
Acta Appl. Math. 63, 27-40 (2000)

Albeverio S, Fei S M
Symplectic geometry on quantum planes
Mod. Phys. Lett. A 14, 549-557 (1999)

Albeverio S, Fei S M , Wang Y
An exactly solvable model of generalized spin ladders
Europhys. Lett. 47, 364-370 (1999)

Albeverio S, Geyler V A
The finite gap property of periodic point potentials
Russ. Math. Surv. 821, Joint session of the Pelinovski Seminar and the Moscow Mathematical Society, announcement (1999)

Albeverio S, Geyler V A, Kostnov O G
Quasi-one-dimensional nanosystems in a uniform magnetic field: explicitly solvable model
Rep. Math. Phys. 44, 1-13 (1999)

Albeverio S, Geyler V A, Margulis V A
Bound states in curved nanostructures
Letts Appl. Phs. J. 26, no. 3 (2000) (in Russian)

Albeverio S, Giese H J, Stabile G
Stochastic and deterministic methods in the analysis of the delta^18 O record in the core V28-239
Chem. Geology 161, 271-289 Special Issue: Earth System Evolution: Geochemical perspective, Ed. L. Veizer (1999)

Albeverio S, Gottschalk H
Scattering theory for quantum fields with indefinite metric
Comm. Math. Phys. 216, no. 3, 491-513 (2000)

Albeverio S, Gottschalk H, Wu J L
Scattering behaviour of quantum vector fields obtained from Euclidean covariant SPDEs
Repts. Math. Phys. 44, 21-28 (1999)

Albeverio S, Gottschalk H, Wu J L
Partly divisible probability measures on locally compact abelian groups
Math. Nachr. 213, 5-15 (2000)

Albeverio S, Hall B C, Sengupta A N
The Segal-Bargmann transform for two-dimensional Euclidean quantum Yang-Mills
Infin. Dimens. Anal. Quantum Probab. Relat. Top. 2, no.1, 27-49 (1999)

Albeverio S, Hilbert A, Kolokoltsov V
Sur le comportement asymptotique du noyau associe a une diffusion degeneree
Comptes Rendus Mathem. - Math. Reports, Academy of Science, Royal Society, Canada 22, no. 4, 151-159 (2000)

Albeverio S, Hu Y Z, Röckner M, Zhou X Y
Stochastic quantization of the two dimensional polymer measure
Appl. Math. Optimiz. 40, 341-354 (1999)

Albeverio S, Karwowski W, Koshmanenko V
On negative eigenvalues of generalized Laplace operators
Repts. Math. Phys. 48, 359-387 (2001)

Albeverio S, Karwowski W, Zhao X L
Asymptotics and spectral results for random walks on p-adics
Stoch. Proc. Appl. 83, 39-59 (1999)

Albeverio S, Khrennikov A, Kloeden E
Memory retrieval as a p-adic dynamical system
BioSystems 49, 105-115 (1999)

Albeverio S, Khrennikov A, Smolyanov O
The probabilistic Feynman-Kac formula for an infinite dimensional Schrödinger equation with exponential and singular potentials
Pot. Anal. 11, 157-181 (1999)

Albeverio S, Klar A
Longtime behaviour of stochastic Hamiltonian systems: the multidimensional case
Potential Anal. 12, no. 3, 281-297 (2000)

Albeverio S, Kondratiev Y, Kozitsky Y V
Classical limits for Gibbs states of quantum lattice models
Letts. Math. Phys. 48, no. 3, 221-233 (1999)

Albeverio S, Kondratiev Y, Minlos R, Shchepannuk G
Ground state euclidean measures for quantum lattice systems on compact manifolds
Rep. Math. Phys. 45, no.3, 419-429 (2000)

Albeverio S, Kondratiev Y, Minlos R, Shchepanyuk G
Uniqueness problems for quantum lattice systems with compact spins
Letts. Math. Phys. 52, no.3, 185-195 (2000)

Albeverio S, Kondratiev Y, Pasurek T
Euclidean Gisbbs states of quantum crystals
Mosc. Math. J. 1, No. 3, 307-313 (2001)

Albeverio S, Kondratiev Y, Röckner M
Diffeomorphism groups, current algebras: configuration space analysis in quantum theory
Rev. Math. Phys. 11, 1-23 (1999)

Albeverio S, Kondratiev Y, Röckner M, Grothaus M
Stochastic dynamics of fluctuations in classical continuous systems
J. Funct. Anal. 185, 129-154 (2001)

Albeverio S, Kondratiev Y, Röckner M, Tsikalenko T
A-priori estimates and existence of Gibbs measures: a simplified proof
CRAS, Paris, 328, Ser. I, 1049-1054 (1999)

Albeverio S, Kondratiev Y, Röckner M, Tsikalenko T
Gibbs states on loop lattices
CRac.Sc. 22, 1-15 (2001)

Albeverio S, Kondratiev Y, Röckner M, Tsikalenko T V
A priori estimates for symmetrizing measures and their applications to Gibbs states
J. Funct. Anal. 171, no. 2, 366-400 (2000)

Albeverio S, Kondratiev Y, Röckner M, Tsikalenko T V
Glauber dynamics for quantum lattice systems
Rev. Math. Phys. 13, no.1, 51-124 (2001)

Albeverio S, Koshmanenko V
Singular rank-one perturbations of self-adjoint operators and Krein theory of self-adjoint extensions
Potent. Anal. 11, 279-287 (1999)

Albeverio S, Koshmanenko V
Form sums approximations of singular perturbations of self-adjoint operators
J. Funct. Anal. 16, 32-51 (1999)

Albeverio S, Koshmanenko V
On the problem of the right Hamiltonian
Rev. Math. Phys. 12, No. 1 (2000)

Albeverio S, Koshmanenko V
On Schrödinger operators perturbed by fractal potentials
Repts. Math. Phys., 45, No. 3, 307-326 (2000)

Albeverio S, Koshmanenko V, Makarov E
General eigenfunctions under singular perturbations
Meth. Funct. Anal. and Top. 5, No 1, 13-28 (1999)

Albeverio S , Kurasov P
Finite rank perturbations and distribution theory
Proc. AMS 127, 1151-1161 (1999)

Albeverio S, Kurasov P
Singular cluster interactions in few-body problems
Lecture Notes in Pure and Appl. Math. 215, 277-292 (2001)

Albeverio S, Makarov K A
Extension of the Ahiezer-Kac determinant formula case of real-valued symbols with two real zeros to the
Acta Appl. Math. 62, no. 2, 155-186 (2000)

Albeverio S, Makarov K A
Ahiezer-Kac's type Fredholm determinants asymptotics for convolution operators with rational symbols
Trans. AMS 353, no. 5, 1985-1993 (2000)

Albeverio S, Minlos R, Sarlatti E, Zhizhina E
Spectral analysis of the disordered 1-D Ising model
Comm. Math. Phys. 204, 651-658 (1999)

Albeverio S, Nizhnik I
Approximation of general zero-range potentials
Ukrain. Mat. Zh. 52, no. 5, 582-589 (2000)

Albeverio S, Rüdiger B, Wu J L
Invariant measures and symmetry property of Levy type operators
Pot. Anal. 13, no. 2, 147-168 (2000)

Albeverio S, Smolyanov O
Representations of solutions to some Schrödinger-Belavkin-type stochastic equations by functional integrals
Dokl. Maths. 59,141-144, No. 1, 1999 (russ. Dokl. Ak. Nauk. 364, No. 1, 747-751, 1999)

Albeverio S, Smolyanov O
Feynman-Kac formulas for evolution differential equations with white-noise-type coefficients
Dokl. Maths. 60, 120-124 (1999) (russ. Dokl. Ak. Nan. 367, 26-30 (1999))

Albeverio S, Steblovskaya V
Asymptotics of infinite-dimensional integrals with respect to smooth measures I
Infin. Dim. Anal. Quant. Prob. 2, 529-556 (1999)

Albeverio S, Ugolini S
Complex Dirichlet forms: non symmetric diffusion processes and Schrödinger operators
Potential Anal. 12, no. 4, 403-417 (2000)

Albeverio S, Zhao X L
On the relation between different constructions of random walks on p-adics
Markov Process. Rel. Fields, 6, No. 2, 239-255 (2000)

Albeverio S, Zhao X L
Measure-valued branching processes associated with random walks on p-adics
Ann. of prob. 28, no.4, 1680-1710 (2000)

Albeverio S, Zhao X L
A decomposition theorem for Levy processes on local fields
J. Theor. Prob.14, no.1, 1-19 (2001)

Albeverio S, Zhou X Y
On the equality of two polymer measures in three dimensions
Tokyo J. Math 5, 561-596 (1999)

Berezansky Y
The works of M.G.Krein on eigenfunction expansion for selfadjoint operators and their applications and development
Operator Theory: Advances and Applications, Vol. 117 (2000), 21-43

Berezansky Y
Spectral theory of commutative Jacobi fields: direct and inverse problems
Fields Inst. Comm., Vol. 25 (2000), 211-224

Berezansky Y
Poisson measure as the spectral measure of Jacobi field
Inf. Dim. Anal. Quantum Prob. Rel. Top., Vol. 3, no. 1 (2000), 121-139

Berezansky Y
Pascal measure on generalized functions and thecorresponding generalized Meixner polynomials
Meth. Funct. Anal. Top., Vol. 8, no. 1 (2002), 1-13

Berezansky Y, Chernobai O B
On the theory of generalized Toeplitz kernels
Ukr. Math. J. , Vol. 52, no. 11 (2000), 1458-1472

Berezansky Y, Kondratiev Y, Kuna T, Lytvynov E
On a spectral representation for correlation measures in configuration space analysis
Meth. Funct. Anal. Top., Vol. 5, no. 4 (1999), 87-100

Berezansky Y, Mierzejewski D
The structure of theextended Fock space
Meth. Funct. Anal. Top., Vol. 6, no. 4 (2000), 1-13

Berezansky Y, Mierzejewski D
The chaotic decomposition for the Gamma fields
Funct. Anal. Appl., Vol. 35, no. 4 (2001), 305-308

Daletskii A, Kondratiev Y, Röckner M
Stochastic Dynamics of Compact Spins: Ergodicity and Irreducibility
Acta Applicandae Mathematicae 63: 27-40 (2000)

Daletskii A, Lytvynov E
Laplace operators and diffusions in tangent bundles over Poisson spaces
1-24, in ``Infinite dimensional stochastic analysis'', Ph. Clement et al, Eds., Neder. Akad. van Wetensh., Amsterdam 2000.

Fei S M
Integrable stochastic ladder models
J. Phys A: Math. Gen. 34, 6545-655 (2001)

Fei S M, Goswami D
Separability of rank two quantum states
Phys. Lett. A, 286, 91-96 (2001)

Fei S M, Kurasov P
Many body problems with ``spin''-related contact interaction
Repts. Math. Phys. 47, 157-166 (2001)

Gesztesy F, Makarov K A, Motovilov A K
Monotonicity and concavity properties of the spectral shift function
Canadian Mathematical Society's Conference Proceedings Series 29, (2000), 207-222

Geyler V A, Margulis V A
Coupled states in a curved nanostructure
Letts. JTP (russ.), 26, No. 2, 99-102 (2000)

Gordon E I, Khrennikov A Y
Finite-dimensional approximations of operators in the Hilbert spaces of functions on locally compact abelian groups
Acta Applic. Math. 64, 33-73 (2000)

Korn R, Schäl M
On value preserving and growth optimal portfolios
Financial optimization. Math. Methods Oper. Res. 50 (1999), no. 2,189-218

Motovilov A K
The structure of the T and S matrix on the unphysical energy sheets for the problem of three quantum particles
Physics of Particles and Nuclei32, Suppl. 1 (2001), 76-79

Motovilov A K, Sandhas W, Belyaev V B
Perturbation of a lattice spectral band by a nearby resonance
J. Math. Phys. 42, (2001), 2490-2506

Nizhnik I
Spatial chaos in a fourth order nonlinear parabolic equation
Phys. Lett. A 288, 299-304 (2001)

Schäl M
Martingale measures and hedging for discrete-time financial markets
Math. Oper. Res. 24 (1999), no. 2, 509-528

Schäl M
Portfolio optimization and martingale measures
INFORMS Applied Probability Conference (Ulm, 1999). Math. Finance 10 (2000), no. 2, 289-303

Schäl M
Price systems constructed by optimal dynamic portfolios
Math. Methods Oper. Res. 51 (2000), no. 3, 375-397

Stummer W, Sturm K T
On exponentials of additive functionals of Markov processes
Stochast. Proc. and their Appl. 85 (2000), 45-60

Sturm K Th
Metric spaces of lower bounded curvature
Expo. Math. 17 (1999), 35-48

Sturm K Th
Monotone approximation of energy functionals for mappingsinto metric spaces. II.
Potential Analysis 11 (1999), 359-386

Sturm K Th
Dirichlet forms and their applications in stochastics, analysis andgeometry
Bulletin of the International Statistical Institute, 52nd Session,Invited Papers, 1999

Sturm K Th
Nonlinear Markov operators associated with symmetric Markov kernels and energy minimizing maps between singular spaces
Calc. Var. Partial Differential Equations 12 (2001), no. 4, 317-357.

Sturm K Th
Nonlinear Markov operators, discrete heat flow, and harmonic maps between singular spaces
Potential Anal. 16 (2002), no. 4, 305-340

Sturm K Th
Nonlinear martingale theory for processes with values in metricspaces of nonpositive curvature
Annals of Probability (2002)

Wu J L
A remark on a hyperfinite flat integral formula for Gaussian measures on l_p
in P. Schuster, U. Berger, H. Osswald, Eds., ``Reuniting the Antipodes - Constructive and Nonstandard Views of the Continuum'', Kluwer Acad. Press, Dordrecht (1999)

Yosida M W
Non-linear continuous maps on abstract Wienerspaces defined on space of tempered distributions
Bulletin of Univ. Electro-Commun., 12, 101 - 117, (1999)


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