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FORSCHUNGSBERICHT 1996-1998


 

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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, Telefax: 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. Atle Hahn
Dipl. Math. Matthias Horst
Dr. Eugene Lytvynov
Dipl. Math. Michael Schmitz

Drittmittelstellen
Dr. Alexei Daletskii (DFG)
Dr. Shao Ming Fei (DFG)
Dr. Martin Grothaus (SFB)
Dipl. Math. Stefan Hußmann (DFG)
Dr. Oleksii Kondratiev (Caesar)
Dipl. Math. Tobias Kuna (GK)
Dipl. Math. Lanjun Lao (WHK)
Dr. Xue Mei Li (A.v.H.)
Prof. Dr. Sylvie Paycha (Av.H.)
Prof. Dr. A. Sengupta (A.v.H.)
Dr. Victoria Steblovskaja (A.v.H.)
Dipl. Phys. Horst Thaler (Österreich, BMW)
PD. Dr. Anton Thalmaier (DFG)
Dipl. Math. Max-Konstantin v. Renesse (SFB)
Dr. Jang-Lung Wu (DFG)
Dr. Xue Lei Zhao (Av.H)

Stipendiaten
Dr. Barbara Rüdiger (TMR(EU) )

Forschungsschwerpunkte
Mathematische Physik : Quantentheorie, Quantenfeldtheorie,Chaostheorie, Hydrodynamik
(Albeverio, Fei, Grothaus, Kondratiev, Sengupta)

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

Mathematisches Modellieren im Bereich Finanzmathematik und Biologie
(Albeverio, Horst, Kondratiev, Lao, Steblovskaja)

Theorie und Anwendung stochastischer Prozeße auf diskrete Strukturen
(Albeverio, Hußmann, Zhao)

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

Funktionalanalysis, Halbgruppentheorie
(Albeverio, Kondratiev, Sturm)

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

Stochastische Analysis
(Albeverio, Li, Steblovskaja)

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

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

Nonstandard Analysis und deren Anwendungen
(Albeverio, Wu)

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

Besondere Forschungsförderung
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)

Veröffentlichungen
Albeverio S., Bogachev L. V., Yarovaya E.B.:
Asymptotics of branching symmetric random walk on the lattice with a single source
C.R. Acad. Sci. I (Math.) (Paris) 326, 975-980, (1998)

Albeverio S., Bogachev L.:
Brownian survival in a clusterized trapping medium
Rev. Math. Phys. 10, 147-189, (1998)

Albeverio S., Bogachev L.:
Localization vs. delocalization of random discrete measures
Th. Prob. Appl. 43, 711-734, (1998)

Albeverio S., Brasche J., Neidhardt H.:
On inverse spectral theory: mixed types of the spectra
J. Funct. Anal. 15, 130-173 (1998)

Albeverio S., Brasche J.F., Koschmanenke V.:
Lippman-Schwinger equations in the singular perturbation theory
Meth.Funct.Anal. Top.3,1-27 (1997)

Albeverio S., Brzezniak Z., Haba Z.:
On the Schrödinger equation with potentials which are Laplace transforms of measures
Pot. Anal. 9, 65-82, (1998)

Albeverio S., Cianci K., Khrennikov A.:
On the Fourier transform and the spectral property of the p-adic momentum and Schrödinger operator
J. Phys. A. 30, 5767-5784, (1997)

Albeverio S., Cianci R., Khrennikov A. Yu.:
Representation of a quantum field Hamiltonian in p-adic Hilbert space
Theor. and Math. Phys. 112 (1997), 1081-1096, (russ.:355-375)

Albeverio S., Cianci R., Khrennikov A.:
On spectrum of the p-adic position operator
J. Phys A-Math Gen. 30: (3), 881-889, (1997)

Albeverio S., Dabrowski L., Kurasov P.:
Symmetries of Schrödinger operators with point interactions
Letts. Math. Phys. 45, 33-47, (1998)

Albeverio S., Daletskii A., Kondratiev Y.:
Some examples of Dirichlet operators associated with the actions of infinite dimensional Lie groups
Meth. Funct. Anal. and Top. No. 2, 1-15, (1998)

Albeverio S., Daletskii A., Kondratiev Yu.:
Infinite systems of stochastic differential equations and some lattice models on compact Riemannian manifolds
Ukr. Math. J. 49, No. 3, 326-338 (1997)

Albeverio S., Daletskii A., Kondratiev Yu.:
Stochastic evolution on product manifolds
Hyperfunctions, operator theory and dynamical systems, Eds. I. Antoniou, G.Lumer; Pitman Res. Notes Vol.399, 274-298, (1998)

Albeverio S., Daletskii A.:
Algebras of pseudodifferential operators in L2 given by smooth measures on Hilbert spaces
Math. Nachr. 192, 5-22, (1998)

Albeverio S., Fei S. M.:
An integral representation for Ising models
Int. J. Mod. Phys. B12,2393-2407, (1998)

Albeverio S., Fei S.M.:
Integrable Poisson Algebras and Two Dimensional Manifolds
J. Phys. A. 31, 1211-1218 (1998)

Albeverio S., Fei S.M.:
Some new exact ground states of generalized Hubbard models
Europhys. Letts. 41, 665-670 (1998)

Albeverio S., Fei S.M.:
Symmetry, integrable chain models and stochastic processes
Rev. Math. Phys. 10, 723-750, (1998)

Albeverio S., Figari R., Orlandi E., Teta A.:
Advances in Dynamical Systems and Quantum Systems
World Scientific, Singapore (1997)

Albeverio S., Gielerak R., Russo F.:
A general setting for stochastic processes associated with operator fields
Stochastic Differential and Differential Equations, Gyor, Hungary, pp. 77-89 (1997), Eds. I Csiszhar, G. Michaletzky; Birkhäuser

Albeverio S., Gielerak R., Russo F.:
Constructive approach to the global Markov property in Euclidean quantum field theory
Markov Processes Relat. Fields 3. 275-322 (1997)

Albeverio S., Gordon E., Khrennikov A.:
Finite dimensional approximations of p-adic pseudodifferentioal operators
Mathematical simulation V.9 No. 10p 11 (1997)

Albeverio S., Gottschalk H., Wu J.L.:
Non trivial scattering amplitudes for some local relativistic quantum field models with infinite metric
Phys. Lett. B, 405, 243-218 (1997)

Albeverio S., Gottschalk H., Wu J.L.:
Partly divisible probability distributions
For. Math. 10, 687-697, (1998)

Albeverio S., Gottschalk H., Wu L.J.:
Models of local relativistic quantum fields with infinite metric (in all dimensions)
Commun. Math. Phys. 184, 509-531 (1997)

Albeverio S., Gottschalk H., Wu L.J.:
Remarks on some new models of interacting quantum fields with infinite metric
Phys. 40, special issue of the Proc. of the 29 th Symp. Math. Phys. Torum (1997)

Albeverio S., Hu Y. Z., Zhou X. Y.:
A remark on non-smoothness of the self-intersection local time of planar Brownian motion
Stat. Prob. Lett. 32:(1), 57-65, (1997)

Albeverio S., Hu Y.Z., Zhou X.Y.:
A remark on non smoothness of the self intersection local time of planar
Letters Prob. Stat. 32, 57-65 (1997)

Albeverio S., Jost J., Paycha S., Scarlatti S.:
A mathematical introduction to string theory
Cambridge University Press (1997)

Albeverio S., Khrennikov A. Yu., De Smedt S., Tirozzi B.:
p-adic dynamical Systems
Theor. and Math. Phys. 114, No 3, 276-287 (russ.:349-365), (1998)

Albeverio S., Khrennikov A. Yu., Kloeden P.:
Human memory and p-adic dynamical systems
Theor. and Math. Phys. 117, Nr.3, 1414-1422 (russ:385-396), (1998)

Albeverio S., Khrennikov A. Yu.:
A regularization of quantum field Hamiltonians with the aid of p-adic number
Acta Appl. Math. 50, 225-251, (1998)

Albeverio S., Khrennikov A.:
A regularization of quantum field Hamiltonians with the aid of p-adic numbers
Acta Appl. Math. 50:(3) 225-251, (1998)

Albeverio S., Kolokoltsov V. N., Smolyanov O. G.:
Continuous quantum measurement: local and global approaches
Rev. math. Phys. 9,907-920 (1997)

Albeverio S., Kolokoltsov V.:
The rate of escape for some Gaussian processes and the scattering theory for their small pertubations
Stoch. Proc. Appl. 67, No. 2 (1997)

Albeverio S., Kondratiev Y. G., Rebenko A. L.:
Peierls argument and long-range order behavior of quantum lattice systems with unbounded spins
J. Stat. Phys. 92, 1137-1152, (1998)

Albeverio S., Kondratiev Y. G., Röckner M., Tsicalenko T.:
Dobrushin's uniqueness for quantum lattice systems with nonlocal interaction
Commun Math. Phys. 189:(2), 621-630, (1997)

Albeverio S., Kondratiev Y., Kozitsky V.:
Critical properties of a quantum hierarchical model
Lett. Math. Phys. 40 pp. 287-291 (1997)

Albeverio S., Kondratiev Y., Kozitsky Y.:
Suppression of critical fluctuations by strong quantum effects in quantum lattice systems
Comm. Math. Phys. 194, 493-512, (1998)

Albeverio S., Kondratiev Y., Röckner M., Tsicalenko T.:
Uniqueness of Gibbs states on loop lattices
C.R. Acad. Sci 324 1401-1406 (1997)

Albeverio S., Kondratiev Y., Röckner M.:
Ergodicity for the stochastic dynamics of quasi-invariant measures with applications to Gibbs states
J. Func. Anal. 149, 415-469 (1997)

Albeverio S., Kondratiev Y., Röckner M.:
Ergodicity of L2-semigroups and extremality of Gibbs states
J. Funct. Anal. 143, 394-423, (1997)

Albeverio S., Kondratiev Yu. G., Minlos R. A.:
Small-mass behavior of quantum Gibbs states for lattice models with unbounded spins
J. Stat. Phys 92, 1153-1172, (1998)

Albeverio S., Kondratiev Yu. G., Röckner M.:
Analysis and geometry on configuration spaces: The Gibbsian case
J. Funct. Anal. 157, 242-291, (1998)

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

Albeverio S., Kondratiev Yu., Kositsky Yu. V.:
Thermodynamic limit theorem for quantum hierarchical model
Lett. Math. Phys. 40, 287-291,(1997)

Albeverio S., Kondratiev Yu., Röckner M., Tsicalenko T.:
Uniqueness of Gibbs states for quantum lattice systems
Prob. Th. Rel. F. 108, 193-218, (1997)

Albeverio S., Kondratiev Yu., Röckner M., Tsicalenko T.V.:
Dobrushin's uniqueness for quantum lattice systems with non-local interaction
Comm. Math. Phys. (Dobrushin Mem. Vol.), 189, 621-630, (1997)

Albeverio S., Kozitsky Yu., Kondratiev Yu.:
Absence of critical points for a class of quantum hierarchical models
Comm. Math. Phys. 187, 1-18 (1997)

Albeverio S., Krüger N., Tirozzi B.:
An extension of Kohonen phonetic maps for speech recognition
Mathem. and Computer Modell. 25(2), (1997)

Albeverio S., Kurasov P.:
Pseudo-differential operators with point interactions
Lett. Math. Phys. 41, pp. 79-92 (1997)

Albeverio S., Kurasov P.:
Rank one pertubations of not semibounded operators
I. Integr. Equat. and Oper. Theory 27 379-400 (1997)

Albeverio S., Kurasov P.:
Rank one pertubations, approximations and selfadjoint extensions
J. Funct. Anal. 146 (1997)

Albeverio S., Lakaev S., Makarov K.A.:
The Efimov effect and an extended Szegö-Kac limit theorem
Lett. Math. Phys. 43, 73-85, (1998)

Albeverio S., Ma Z.M., Röckner M.:
Partition of unity for Sobolev spaces in infinite dimensions
J. Funct. Anal. 143, 247-268 (1997)

Albeverio S., Makarov K.:
Limit behavior in a singular perturbation problem, regularized convolution operators and the 3-body quantum problem
pp. 1-10 in Differential and Integral Operators, Proc. IWOTA 95, Eds.: I. Gohberg, P. Mennicke, C. Tretter, Birkhäuser, Basel (1998)

Albeverio S., Makarov K.A.:
Non trivial attracts in a model related to the three body problem
Acta. Appli. Math. 48, 113-184 (1997)

Albeverio S., Morato L., Ugolini S.:
Non-symmetric diffusions and related Hamiltonians
Pot. Anal. 8, 195-204 (1998)

Albeverio S., Russo F.:
Stochastic partial differential equations, infinite dynamical stochastic processes and random fields: a short introduction
pp 68-87 in Non-linear Klein-Gordon and Schrödinger systems: theory and applications (1997); Eds.: Vazquez L., Streit V., Pèrez-Garzia V. M.

Albeverio S., Sengupta A.:
A mathematical construction of the non-abelian Chern-Simons functional integral
Commun. Math. Phys. 186, 563-579 (1997)

Albeverio S., Sengupta A:
The Chern-Simons functional integral as an infinite-dimensional distribution
Nonlinear Anal.-Theor. 30:(1) 329-335, (1997)

Albeverio S., Smolyanov O.G., Shavgulidze E.T.:
Some methods for quantizing finite-dimensional Hamiltonian systems with constraints
Dokl. Maths. 58, No.1, 114-117, (1998)

Albeverio S., Smolyanov O.G.:
Infinite-dimensional stochastic Schrödinger-Belavkin equations
Russ. Math. Surv.+ 52: (4), 822-823, (1997)

Albeverio S., Smolyanov O.G.:
The Liouville theorem for finite dimensional Hamilton-Dirac systems
Dokl. Akad. Nauk. 355, No. 1, 7-10 (1997)(russ.) (transl. Dokl. Math. 56, 475-478 (1997)

Albeverio S., Tirozzi B.:
Asymmetric neural networks and immune system
Markov Proc. Rel. Fields 3, 423-442 (1997)

Albeverio S., Tirozzi B.:
Introduction to the matematical theory of neural networks
197-222 in Fourth Granada Lectures (1997); Eds.:Garrido P.L., Marro J., Springer Berlin

Albeverio S., Wu J. L., Zhang T. S.:
Parabolic SPDE's driven by Poisson noise
Stoch. Proc. Appl. 74, 21-36, (1998)

Albeverio S., Wu J.L.:
On the lattice approximation for certain generalized vector Markov fields in four space-time dimensions
Acta Appl. Math. 47, 31-48, (1997)

Albeverio S., Wu. L.J.:
On the lattice approximation for certain generalized vector Markov fields in four space-time dimensions
Acta Appl. Math. 47, 31-48 (1997)

Albeverio S., Zhang T.S.:
Approximations of Ornstein-Uhlenbeck processes with unbounded linear drifts
Stochastics and Stochastics Reports vol63, No.3-4, 303-312, (1998)

Albeverio S.:
Some applications of infinite dimensional analysis in mathematical physics
Helv. Phys. Acta 70 pp. 479-506 (1997)

Albeverio S.:
Some remarks on fractals and dynamical systems in biology
pp 152-169 in Proc. ; Eds.: Losa G., Merlini D., Nonnenmacher Th., Weibel E.; Birkhäuser Basel (1997)

Albeverio S.:
Wiener and Feynman-Path integrals and their applications
pp. 163-194 in Proc. N. Wiener Centenary Conference, East Lansing, 1994, Proceedings of Symposia in Apllied Mathematics, vol. 52 Edts. P. Masani et al, AMS (1997)

Schäl, M.:
Martingale measures and hedging for discrete-time financial markets.
accepted for publication in Math. Oper. Research (1996)

Schäl, M.:
On piecewise deterministic Markov control processes : Control of jumps and of risk processes in insurance.
Insurance : Mathematics and Economics 22 75-91

Sturm, E.M. Ouhabaz, P. Stollmann, J. Voigt:
The Feller property for absorption semigroups
J. Funct. Anal. 138 (1996), 351-378

Sturm, R. Höhnle:
On the conservativeness of space-time process.
In "Probability and Mathematical Statistics (Proceedings of the 7th Japan-Russia Symposium 1995)", ed by S.Watanabe, M. Fukushima, Yu. V. Prohorov and A.N. Shiryaev. World Scientific 1996

Sturm:
Analysis on local Dirichlet spaces - III. The parabolic Harnack inequality.
J. Math. Pures Appl. 75 (1996), 273-297

Sturm:
Is a diffusion determined by its intrinsic metric?
Chaos Solitons Fractals 8 (1997), 1855-1866

Sturm:
Monotone approximation of energy functionals for mappings into metric spaces.
I. J. reine angew. Math. 486 (1997), 129-151

Sturm:
Diffusion processes and heat kernels on length spaces.
Annals of Probab. 26 (1998), 1-55

Sturm:
How to construct diffusion processes on metric spaces.
Potential Analysis 8 (1998), 149-161

Sturm:
The geometric aspect of Dirichlet forms.
In: "New directions in Dirichlet forms." (Ed. by J.Jost, W. Kendall, U, Mosco, M. Röckner, K.T. Sturm) International Press and AMS 1998


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