Erschienen seit 1998:

• Buckwar, E.; Luchko, Y.
  Invariance of a Partial Differential Equation of Fractional Order under the Lie Group of Scaling Transformations
  Journal of Mathematical Analysis and Applications (1998), 227, 81-97.
  
• Föllmer, H.; Küchler, U.
  Richard von Mises, in Mathematics in Berlin, (Eds. H.G.W. Begehr, H. Koch, J. Kramer, N. Schappacher, E.-J. Thiele)
  Birkhäuser Basel (1998), 111-116
• Küchler, U.; Sørensen, M.
  On Exponential families of Markov processes
  Journal of Statist. Planning and inference 66 (1998), pp. 3-19

1999:

• Gushchin, A.; Küchler, U.
  Asymptotic Properties of Maximum-Likelihood-Estimatiors for a Class of Linear Stochastic Differential Equations with Time Delay
  Bernoulli 5(6) (1999), 1059-1098 
• Küchler, U.; Neumann,K., Sørensen M., Streller,A.
  Stock Returns and Hyperbolic Distributions
  Mathematical and Computer Modelling 29, 1999, pp. 1-15, Pergamon Press, edit. by Mittnik, Rachev
• Küchler, U.; Sørensen, M.
  A Note on Limit Theorems for Multivariate Martingales
  Bernoulli 5(3) (1999), pp. 483-493

  2000:
  

• Baker, CTH.; Buckwar, E.
  Continuous Theta-methods for the Stochastic Pantograph Equation
  Electronic Transactions on Numerical Analysis (2000), 11:131-151.
• Baker, CTH.; Buckwar, E.
  Numerical Analysis of Explicit One-step Methods for Stochastic Delay Differential Equations
  LMS-Journal of Computational Mathematics (2000), 3: 315-335.
• Buckwar, E.
  Introduction to the Numerical Analysis of Stochastic Delay Differential Equations
  Journal of Computational and Applied Mathematics (2000), 125, pp. 297-307.
• Buckwar, E.
  On a Nonlinear Volterra Integral Equation Proceedings of the Volterra Centennial Symposium, Arlington, Texas, USA, 23.- 25.5. 1996
  (eds: C. Corduneanu and I.W.Sandberg) Gordon and Breach Science Publishers, (2000).
• Gushchin, A.; Küchler, U.
  On Stationary Solutions of Delay Differential Equations Driven by a Lévy Process
  Stochastic Processes and their Applications 88, 2000,. 195-211.
• Küchler, U.; Kutoyants, Y.
  Delay Estimation for some Stationary Diffusion-type Processes
  Scandinavian Journal of Statistics 27 (3) (2000), 405-414
• Küchler, I.; Küchler, U.; Thiele, S.; Wernecke, K.-D.; Winter, H.;
  The Process of Metastases Formation by Melanoma Patients during the Aftercare - Modelling with Markov Chains and Cox's Regression
  Biometrical Journal 42 (2000) 2, 161-170
• Küchler, U.; Platen, E.
  Strong Discrete Time Approximation of Stochastic Differential Equations with Time Delay
  Mathematics and Computer Simulation 54 (2000), 189-205
  

  2001:
  

• Gushchin, A.; Küchler, U.
  Addendum to "Asymptotic Inference for a Linear Stochastic Differential Equation with Time Delay"
  Bernoulli, 7 (2001), 629-632 
• Jaschke, St.; Küchler, U.
  Coherent Risk Measures and good-deal bounds
  Finance and Stochastics, 5 (2001), 181-200
• Küchler, U.; Vasil'iev, V.A.
  On sequential parameter estimation for some linear stochastic differential equations with time delay
  Sequential Analysis, 20 (3) (2001a), 117-146
  
• Riedle, M.; Steinebach, J.
  Variance estimation in the change analysis of a linear regression model, Metrika 54(2), 2001, 139 - 157

  2002:
  

• Küchler, U.; Naumann, E.
  On the Heath-, Jarrow-Morton-Model of Termstructures driven by Lévy-Processes
  Discussion Paper des SFB 373 (2002).
  
• Küchler, U.; Platen, E.
  Weak Discrete Time Approximation of Stochastic Differential Equations with Time Delay
  Mathematics and Computer Simulations (2002) 59, 497-507
• Küchler, U.; Vasiljev, V.A.
  Sequential Identification of linear Dynamic Systems with time delay
  Discussion Paper des SFB 373 (2002).
• Reiss, M.
  Minimax rates for nonparametric estimation of the drift functional in affine stochastic delay equations
  Statistical Inference for Stochastic Processes 5, No.2, 131-152 (2002).
  
• Riedle, M.
  Lyapunov exponents for linear delay equations in arbitrary phase spaces, Discussion Paper No60,
  Sonderforschungsbereich 373, Humboldt University of Berlin, (2002)

  2003:
  
  

• Gushchin, A.; Küchler, U.
  On parametric statistical models for stationary solutions of affine stochastic delay differential equations
  Mathematical Methods of Statistics, New York, 12(1), (2003), 31-61
• Küchler, U.; Vasiljev, V.A.
  On ensured parametric estimation of a diffusion process with time delay.
  Proceedings of the 13th IFAC Symposium on System Identification 'SYSID-2003',
  Rotterdamm, Netherlands (2003), 1217-1221
  
• Riedle, M.
  Stochastische Differentialgleichungen mit unendlichem Gedächtnis (Stochastic differential equations with infinite
  delay), Ph.d. thesis, Humboldt University of Berlin, (2003)

  2004:
  
  

• Buckwar, E.
  The Theta-Maruyama scheme for stochastic functional differential equations with distributed memory term.
  Monte Carlo Methods and Applications Vol.10, No.3-4,  235--244, (2004). Preprint 
• Buckwar, E.; Winkler, R.
  On Two-step Schemes for SDEs with Small Noise. PAMM  Proc. Appl. Math. Mech. 4, 15--18, (2004). 
• Gushchin, A.; Küchler, U.
  On recovery of a measure from its symmetrization. Theory Probab. Appl., v.49 (2004), 352-362   
• Gushchin, A.; Küchler, U.
  On Oscillations of the geometric Brownian motion with time-delayed drift.
  Statistics & Probability Letters 70 (2004) 19-24
  
• Küchler, U.
  On integrals with respect to Lévy processes, Statistics and Probability Letters 66 (2004), 145-151
• Küchler, U.; Vasiljev, V.A.
  Sequential identification of linear dynamic systems with memory.
  Statistical Inference of Stochastic Processes (2005) VIII, (1), 1-24
• Reiss, M.; Hoffmann, M.; Cohen, A.
  Adaptive Wavelet-Galerkin Methods for Linear Inverse Problems
  SIAM Journal on Numerical Analysis42, No.4, 1479-1501 (2004)
• Reiss, M.; Hoffmann, M.; Gobet, E.
  Nonparametric Estimation of Scalar Diffusions Based on Low-Frequency Data
  The Annals of Statistics, 32, No.5, 2223-2253 (2004)
  

  2005:
  
  

• Appleby, J.A.D.; Buckwar, E.
  Noise Induced Oscillation in Solutions of Stochastic Delay Differential Equations,
  Dynamic Systems and Applications 14(2), pp. 175–196, (2005)
• Baker, C.; Buckwar, E.
  Exponential Stability in p-th Mean of Solutions, and of Convergent Euler-type Solutions, of Stochastic Delay Differential Equations
  Preprint (gzipped). Journal of Computational and Applied Mathematics. In Press, available online 19 March 2005.
  
• Baker, C.; Buckwar, E.
  On Halanay-Type Analysis of Exponential Stability for the theta-Maruyama Method for Stochastic Delay Differential Equations. Preprint
  Accepted in Stochastics & Dynamics.
• Buckwar, E.
  Existence and Uniqueness of Solutions of Abel Integral Equations with Power-law Non-linearities.
  Accepted in Nonlinear Analysis.
• Buckwar, E.
  One-Step Approximations for Stochastic Functional Differential Equations.  Preprint, Accepted in Applied Numerical Mathematics
• Buckwar, E.; Kuske, R.; L'Esperance, B.; Soo, T.
  Noise-Sensitivity in Machine Tool Vibrations. Preprint Accepted in International Journal of Bifurcations and Chaos.
• Buckwar, E.; Shardlow, T.
  Weak approximation of stochastic differential delay equations
  IMA J. Numerical Analysis, 25, 57--86, (2005).
• Gapeev P., Küchler, U.
  On Markovian Short Rates in Term Structure Models Driven by Jump-Diffusion Processes.
  Submitted to Statistics & Decision (2005).
  
• Küchler, U., Vasiliev, V.A.
  On guaranteed parameter estimation of stochastic differential equations with time delay by noisy observations
  Discussion Paper des SFB 373 Nr. 14 (2005) to appear in Journal of Statist. Planning and Inference
• Küchler, U., Vasiliev, V.A.
  Sequential identification of linear dynamic systems with memory.
  Statistical Inference of Stochastic Processes (2005) VIII, (1), 1-24
  
• Reiss, M.
  Adaptive estimation for affine stochastic delay differential equations
  Bernoulli 11, No.1, 67-102 (2005).
  
• Riedle, M.
  Lyapunov Exponents for Linear Delay Equations in arbitrary Phase Spaces
  to appear in Integral Equations and Operator Theory.
  

  2006:
  

• Appleby, J. A. D.; Riedle, M.
  Almost sure asymptotic stability of Volterra integro-differential equations with fading perturbations
  Stochastic analysis and applications 24, 4, 813-826 (2006).
  
• Buckwar, E.; Horvath Bokor, R.; Winkler, R.
  Asymptotic mean-square stability of two-step methods for stocastic ordinary differential equations,
  Preprint 04-25 (PDF-file), BIT Numerical Mathematics 46(2), 261 - 282, (2006).
  
• Buckwar, E.; Winkler, R.
  Multi-step methods for SDEs and their application to problems with small noise.
  Preprint (PDF-file),  SINUM 44(2),  779--803, (2006).
  
• Buckwar, E.; Winkler, R. 
  Improved linear multi-step methods for stochastic ordinary differential equations. Preprint (PDF-file)
  Accepted in Journal of Computational and Applied Mathematics, available online 10 August 2006
• van Gaans, O.; Reiß, M.; Riedle, M.
  Delay differential equations driven by Levy process: stationarity and Feller properties
  Stochastic processes and their applications 116, 1409-1432 (2006)
• Mao, X.; Riedle, M.
  Mean square stability of stochastic Volterra integro-differential equations
  Systems and Control Letters, 55, 459-465 (2006).
• Riedle, M.
  Lyapunov exponents for linear delay equations in arbitrary phase spaces
  Integral equations and operator theory 54, 259-278 (2006).
  

  2007:
  

• Buckwar, E.; Winkler, R. 
  Multi-step Maruyama methods for stochastic delay differential equations. Preprint (PDF-file)
  to appear in Stochastic analysis and applications
• van Gaans, O.; Reiß, M.; Riedle, M.
  On Emery's inequality and a variation-of-constants formula ,
  to appear in Stochastic analysis and applications
• van Neerven, J. M. A. M. ; Riedle M.
  Solutions of stochastic delay equations in spaces of continuous functions, (with J. M. A. M. van Neerven) ,
  to appear in  Semigroup forum
  

Betreute und abgeschlossene Dissertationen:

• Metzner, G.
  Zinsswaps und Ausfallriskante Anleihen in Deutschland
  Dissertation, Wirtschaftswissenschaftliche Fakultät, Humboldt-Universität zu Berlin (2000).
  gemeinsam betreut mit TP C1 (Stehle).
• Putschke, U.
  Stochastische Funktionaldifferentialgleichungen und lokal-asymptotische Eigenschaften ihrer Parameterschätzungen
  Dissertation, Inst. f. Mathematik, Humboldt-Universität zu Berlin, 190 Seiten (2001).
• Reiß, M.
  Nonparametric Estimation for Stochastic Delay Differential Equations
  Dissertation, Inst. f. Mathematik, Humboldt-Universität zu Berlin, 123 Seiten (2002).
• Riedle, M.
  Stochastische Differentialgleichungen mit unendlich langem Gedächtnis
  Institut für Mathematik, Humboldt-Universität zu Berlin, 162 Seiten (2003).
• Lorenz, R.
  Weak Approximation of Stochastic  Delay Differential Equations with Bounded Memory by Discrete Time Series
• Tappe, S.
  Finite Dimensional Realizations for Term Structure Models Driven by Semimartingales
  

Diplomarbeiten (Auswahl)

• Schwarz, Ch.
  Über affine Differentialgleichungen mit Gedächtnis und ihre charakteristischen Gleichungen (1999).
• Gilsing, H.
  Einige Eigenschaften stochastischer Differentialgleichungen mit Gedächtnis (2000).
• Groß, U.
  Zufällige Irrfahrten mit Zeitverzögerung (2002).
• Ganzhorn, T.
  Das Bass-Modell für die Ausbreitung von Innovationen und seine Erweiterung durch Stochastik und Zeitverzögerungen (2004).
• Ignatieva, E.
  Das Bass Modell für die Ausbreitung von Innovationen - Seine Analoga für kleine Märkte mit abhängigen Teilnehmern (2006)

Preprints und weitere eingereichte Arbeiten

• Gilsing, H.; Küchler, U.; Platen, E.
  Über die Stabilität des Euler-Schemas für eine Affine Stochastische Differentialgleichung mit Gedächtnis
  Discussion Paper des SFB 373 Nr. 20 (2001) (PS.Z, (PDF.ZIP)).
• Riedle, M.
  Affine Stochastic Differential Equations with Infinite Delay on Abstract Phase Spaces
  Discussion Paper des SFB 373 Nr. 99 (2001).
  
  
• Gilsing, H.
  On Lp-stability of numerical schemes for Affine Stochastic Delay Differential Equations: stochastic recurrance relations
  Discussion Paper des SFB 373 Nr. 59 (2002) (PS.ZIP, PDF.ZIP)). 
• Gilsing, H.
  On stability of an affine SDDE
  Forthcoming Discussion Paper des SFB 373
• Gilsing, H.
  On the computation of stability regions for affine SDDE
  Forthcoming Discussion Paper des SFB 373.
• Küchler, U.; Platen, E.
  Weak Discrete Time Approximation of Stochastic Differential Equations with Time Delay,
  Discussion Paper 30, (2001) Sonderforschungsbereich 373, Humboldt-Universität zu Berlin,
  to appear in Mathematics & Computer Simulation (2992)
  
• Küchler, U.; Soerensen, M.
  Statistical inference for discrete-time samples from linear stochastic delay equations
  Manuskript, 9 Seiten (2002).
  
  
• Appleby, J.; Buckwar, E.
  Sufficient conditions for polynomial asymptotic behaviour of the stochastic pantograph equation. Preprint
  (submitted 2003)
  
  
• Buckwar, E.; Winkler, R.
  Multi-step methods for SDEs and their application to problems with small noise.  Preprint
  (submitted 2004)
  
  
• Buckwar, E.; Kuske; Mohammed, R.S.-E.; Shardlow, T.
  The Weak Euler Scheme for Stochastic Delay Equations,  submitted to Mathematics of Computation.
  
• Buckwar, E.; Winkler, R.
  Improved Two-step Methods for SDEs with Small Noise, submitted to  Journal of Computational and Applied Mathematics,
  Revision angefordert.
  
  
• Appleby, J. A. D.; Mao, X.; Riedle, M.
  Geometric Brownian Motion with delay: mean square characterisation,
  submitted 2007, Preprint 06-27, 2006, Institute of Mathematics, Humboldt University of Berlin
• Appleby, J. A. D.; Riedle, M.
  Stochastic Volterra differential equations in weighted spaces, (with J. A. D. Appleby) ,
  submitted 2007
• van Gaans, O.; Riedle, M.
  Stochastic Integration for Levy Processes with Values in Banach Spaces,
  submitted 2007
• Riedle, M.
  Solutions of affine stochastic functional differential equations in the state space ,
  submitted 2007 , Preprint 05-3, 2005, Institute of Mathematics, Humboldt University of Berlin

Letzte Änderung: 03.04.2007, Katja Krol