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).
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)
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.; 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.
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.
Küchler, U., Gapeev, P.
On Markovian Short Rates in Term Structure Models Driven by
Jump-Diffusion Processes.
Submitted to Statistics & Decision (2005).
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).
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
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
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).
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
Master thesis
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 and
submitted manuscripts
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)).
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.