Chair of Stochastics and its Applications
Publications

Publications

Publications in Peer Reviewed Journals and Conference Proceedings

Müller-Gronbach, T., Yaroslavtseva, L. (2017). On sub-polynomial error bounds for quadrature of SDEs with bounded smooth coefficients. Stochastic Analysis and Applications 35, 423-451.

Jentzen, A., Müller-Gronbach, T.,  Yaroslavtseva, L. (2016). On stochastic differential equations with arbitrary slow convergence rates for strong approximation. Communications in Mathematical Sciences  14, 1477-1500.

Müller-Gronbach, T., Yaroslavtseva, L. (2016). Deterministic quadrature formulas for SDEs based on simplified weak Ito-Taylor steps. Foundations of Computational Mathematics 16, 1325-1366.

Dereich, S., Müller-Gronbach, T. (2015). Quadrature for self-affine distributions on Rd. Foundations of Computational Mathematics 15, 1465-1500.

Müller-Gronbach, T., Ritter, K., Yaroslavtseva, L. (2015). On the complexity of computing quadrature formulas for marginal distributions of SDEs. Journal of Complexity 31, 110-145.

Altmayer, M., Dereich, S., Li, S., Müller-Gronbach, T., Neuenkirch, A., Ritter, K., Yaroslavtseva, L. (2014). Constructive Quantization and Multilevel Algorithms for Quadrature of Stochastic Differential Equations. In: Extraction of Quantifiable Information from Complex Systems (Dahlke, S., Dahmen, W., Griebel, M., Hackbusch, W., Ritter, K. Schneider, R., Schwab, C., Yserentant, H., eds.), Lecture Notes in Computational Science and Engineering, Springer International Publishing, 109-132.

Müller-Gronbach, T., and K. Ritter (2013). A local refinement strategy for constructive quantization of scalar SDEs.  Foundations of Computational Mathematics 13, 1005-1033.

Dereich, S., Müller-Gronbach, T. and K. Ritter (2013). On the Complexity of Computing Quadrature Formulas for SDEs (invited survey paper). Foundations of Computational Mathematics, Budapest 2011 (F. Cucker, T. Krick, A. Pinkus, A. Szanto, eds.), LMS Lecture Notes, Cambridge University Press, Cambridge, 72-92.

Müller-Gronbach, T., Ritter, K., Yaroslavtseva, L. (2012). Derandomization of the Euler scheme for scalar stochastic differential equations. J. Complexity 28, 139-153.

Hickernell, F. J., Müller-Gronbach, T., Niu, B. and K. Ritter (2011). Multi-level Monte Carlo algorithms for infinite-dimensional integration on RN. J. Complexity 26, 229-254

Hickernell, F. J., Müller-Gronbach, T., Niu, B. and K. Ritter (2010). Deterministic Multi-level Algorithms for infinite-dimensional integration on RN. J. Complexity 27, 331-351

Creutzig, J., Dereich, S., Müller-Gronbach, T. and K. Ritter (2009). Infinite-Dimensional Quadrature and Approximation of Distributions. Foundations of Computational Mathematics 9, 391-421.

Müller-Gronbach, T. and K. Ritter (2009). Variable Subspace Sampling and Multi-level Algorithms (invited survey paper). Monte Carlo and Quasi-Monte Carlo Methods 2008 (P. L'Ecuyer, A.B. Owen, eds.), Springer-Verlag, Berlin, 131-156.

Müller-Gronbach, T., Ritter, K. and T. Wagner (2008b). Optimal pointwise approximation of infinite-dimensional Ornstein-Uhlenbeck processes. Stochastics and Dynamics 8, 519-541.

Müller-Gronbach, T. and K. Ritter (2008). Minimal errors for strong and weak approximation of stochastic differential equations (invited survey paper). Monte Carlo and Quasi-Monte Carlo Methods 2006 (A. Keller, S. Heinrich, H. Niederreiter, eds.), Springer-Verlag, Berlin, 53-82.

Müller-Gronbach, T., Ritter, K. and T. Wagner (2008a). Optimal pointwise approximation of a linear stochastic heat equation with additive space-time white noise. Monte Carlo and Quasi-Monte Carlo Methods 2006 (A. Keller, S. Heinrich, H. Niederreiter, eds.), Springer-Verlag, Berlin, 577-589.

Creutzig, J., Müller-Gronbach, T. and K. Ritter (2007). Free-knot spline approximation of stochastic processes. Journal of Complexity 23, 867-889.

Müller-Gronbach, T. and K. Ritter (2007). An Implicit Euler Scheme with Non-uniform Time Discretization for Heat Equations with Multiplicative Noise. BIT Numerical Mathematics 47, 393-418.

Müller-Gronbach, T. and K. Ritter (2007). Lower bounds and non-uniform time discretization for approximation of stochastic heat equations. Foundations of Computational Mathematics 7, 135-181.

Hofmann, N. and T. Müller-Gronbach (2006). A modified Milstein scheme for approximation of stochastic delay differential equations with constant time lag. Journal of Computational and Applied Mathematics 197, 89-121.

Müller-Gronbach, T. (2004). Optimal Pointwise Approximation of SDE's based on Brownian Motion at Discrete Points. Annals of Applied Probability 14, 1605-1642.

Hofmann, N. and T. Müller-Gronbach (2004). On the Global Error of Ito-Taylor Schemes for Strong Approximation of Stochastic Differential Equations. Journal of Complexity 20, 732-752.

Müller-Gronbach, T. (2002). Optimal Uniform Approximation of Systems of Stochastic Differential Equations. Annals of Applied Probability 12, 664-690.

Hofmann, N., Müller-Gronbach, T. and K. Ritter (2002). Linear vs. Standard Information for Scalar Stochastic Differential Equations. Journal of Complexity 18, 394-414.

Hofmann, N., Müller-Gronbach, T. and K. Ritter (2001). The Optimal Discretization of Stochastic Differential Equations. Journal of Complexity 17, 117-153.

Hofmann, N., Müller-Gronbach, T. and K. Ritter (2000b). Step-Size Control for the Uniform Approximation of Systems of Stochastic Differential Equations with Additive Noise. Annals of Applied Probability 10, 616-633.

Hofmann, N., Müller-Gronbach, T. and K. Ritter (2000a). Optimal Approximations of Stochastic Differential Equations by Adaptive Step-Size Control. Math. Comp. 69, 1017-1034.

Müller-Gronbach, T. and K. Ritter (1998). Spatial Adaption for Predicting Random Functions. Annals of Statistics 26, No. 6, 2264-2288.

Müller-Gronbach, T. (1998). Hyperbolic Cross Designs for Approximation of Random Fields. J. Statist. Plann. Inference 66, 321-344.

Emmerich, F. and T. Müller-Gronbach (1998). A law of the iterated logarithm for discrete discrepancies and its applications to pseudorandom vector sequences. Statistics. 32, 75-85.

Müller-Gronbach, T. and K. Ritter (1997). Uniform reconstruction of gaussian processes. Stochastic Processes Appl. 69, 55-70.

Müller-Gronbach, T. and R. Schwabe (1996). On optimal allocations for estimating the surface of a random field. Metrika 44, 239-258.

Müller-Gronbach, T. (1996). Optimal designs for approximating a stochastic process with respect to a minimax criterion. Statistics 27, 279-296.

Müller-Gronbach, T. (1996). Optimal designs for approximating the path of a stochastic process. J. Statist. Plann. Inference 49, 371-385.

Müller-Gronbach, T. (1994). Asymptotically optimal designs for approximating the path of a stochastic process with respect to the L-Norm. Tatra Mountains Mathematical Publications 7, 87-95.

Müller-Gronbach, T. (1994). Comment on `The Theory of Search from a Statistical Viewpoint' by H. P. Wynn and A. Zhiligljavsky. Test, Vol. 3, No. 2, 35-36.

Submitted Papers

Dereich, S., Müller-Gronbach, T. (2017). General multilevel adaptations for stochastic approximation algorithms. Preprint. arXiv:1506.05482

Müller-Gronbach, T., Yaroslavtseva, L. (2017). A Note on strong approximation of SDEs with smooth coefficients that have at most linearly growing derivatives. Preprint. arXiv:1707.08818

Hefter, M., Herzwurm, A., Müller-Gronbach, T. (2017). Lower error bounds for strong approximation of scalar SDEs with Non-Lipschitzian coefficients. Preprint. arxiv:1710.08707

Books

Müller-Gronbach, T., Novak, E. and K. Ritter (2012) . Monte Carlo-Algorithmen. Springer-Lehrbuch, Springer Berlin.

Lehn, J., Müller-Gronbach, T. and S. Rettig (2000). Einführung in die Deskriptive Statistik. Teubner, Leipzig.

Further Publications

Grycko, E. and T. Müller-Gronbach (2008). A Kernel Pressure Estimator and the Law of Atmospheres. Applied and Computational Mathematics 7, 84-88.

Doede, T., Cornely, D. and T. Müller-Gronbach (2001). A protocol for the qualitative assessment of colonic transit. Zentralblatt für Kinderchirurgie, 10, 25-29.

Lehn, J., Müller-Gronbach, T. and S. Rettig (1997). Lorenzkurve und Gini-Koeffizient zur statistischen Beschreibung von Konzentration. Der Mathematikunterricht, Jahrgang 43, Heft 4, 36-46.

Theses

Müller-Gronbach, T. (2002). Strong Approximation of Systems of Stochastic Differential Equations. Habilitationsschrift. Technische Universität Darmstadt.

Müller-Gronbach, T. (1992). Optimierung von Experimenten zur Schätzung von Pfaden stochastischer Prozesse. Dissertation. Freie Universität Berlin.

Müller-Gronbach, T. (1990). Repeated Measurement Designs. Diplomarbeit. Freie Universität Berlin.