# Martin Redmann - Personal Homepage

I am working within the research group Stochastic Algorithms and Nonparametric Statistics at the Weierstraß Institute for Applied Analysis and Stochastics.

I am a member of the DFG Research Unit - Rough Paths, Stochastic Partial Differential Equations and Related Topics and I am a postdoctoral researcher within the subproject Numerical Analysis of Rough PDEs. I am also a part of the research group Quantitative analysis of stochastic and rough systems. From August 2018 to January 2019 I was an Interim Professor at the University of Southern Denmark.

## Research Interests

- Numerical Approximations to Rough (P)DEs
- Lévy Processes
- Stochastic Ordinary Differential Equations
- Stochastic Evolution Equations
- Model Reduction for Stochastic Systems
- Balanced Truncation for Linear Controlled Stochastic Differential Equations with Lévy Noise
- Singular Perturbation Approximation for Linear Controlled Stochastic Differential Equations with Lévy Noise
- Error Bound and Stability Analysis for Model Order Reduction Methods for Stochastic Systems
- Galerkin Schemes for Controlled Stochastic Partial Differential Equations with Lévy Noise

## Short CV

**since 02/2019**Weierstraß Institute for Applied Analysis and Stochastics in Berlin, Postdoctoral researcher in mathematics**08/2018 − 01/2019**University of Southern Denmark (Odense): Department of Mathematics and Computer Science, Interim Professor**07/2016 − 07/2018**Weierstraß Institute for Applied Analysis and Stochastics in Berlin, Postdoctoral researcher in mathematics**06/2012 − 06/2016**Max Planck Institute for Dynamics of Complex Technical Systems in Magdeburg, Ph.D. student in mathematics, Ph.D. thesis:*Model Order Reduction Techniques Applied to Evolution Equations with Lévy Noise***10/2009 − 04/2012**Martin-Luther-Universität Halle-Wittenberg, Studies in Mathematics (major) and Economics (minor) with main focus on stochastics, Degree: Master of Science, Masters' thesis: Zur Stochastischen Analysis Hilbertraum-wertiger Lévy-Prozesse (The Stochastic Analysis of Hilbert Space-valued Lévy Processes)**10/2006 − 09/2009**Martin-Luther-Universität Halle-Wittenberg, Studies in Mathematics (major) and Economics (minor), Degree: Bachelor of Science, Bachelor thesis: Ein zeitdiskretes fraktales Filterproblem (A Time Discrete Fractional Filtering Problem)

## Preprints

- M. Redmann,
*An L*, Submitted 2019^{2}_{T}-error bound for time-limited balanced truncation - M. Redmann,
*A new type of singular perturbation approximation for stochastic bilinear systems*, Submitted 2019 - C. Bayer, M. Redmann, J. Schoenmakers,
*Dynamic programming for optimal stopping via pseudo-regression*, Submitted 2019 - C. Bayer, D. Belomestny, M. Redmann, S. Riedel, J. Schoenmakers,
*Solving linear parabolic rough partial differential equations*, Submitted 2019

## Publications

- P. Goyal, M. Redmann,
*Time-Limited H*, Applied Mathematics and Computation, 2019_{2}-Optimal Model Order Reduction - M. Redmann,
*Energy estimates and model order reduction for stochastic bilinear systems*, International Journal of Control, 2018 - M. Freitag and M. Redmann,
*Balanced Model Order Reduction for Linear Random Dynamical Systems Driven by Lévy Noise*, Journal of Computational Dynamics, 2018 - P. Kürschner, M. Redmann,
*An Output Error Bound for Time-Limited Balanced Truncation*, Systems and Control Letters, 2018 - M. Redmann,
*Type II balanced truncation for deterministic bilinear control systems*, SIAM Journal on Control and Optimization, 2018 - M. Redmann,
*Type II singular perturbation approximation for linear systems with Lévy Noise*, SIAM Journal on Control and Optimization, 2018 - P. Benner and M. Redmann,
*Singular Perturbation Approximation for Linear Systems with Lévy Noise*, Stochastics and Dynamics, 2017 - P. Benner and M. Redmann,
*An H*, Systems and Control Letters, 2017_{2}-Type Error Bound for Balancing-Related Model Order Reduction of Linear Systems with Lévy Noise - P. Benner, P. Goyal, and M. Redmann,
*Truncated Gramians for Bilinear Systems and their Advantages in Model Order Reduction*, Model Reduction of Parametrized Systems,*MS&A - Modeling, Simulation and Applications*, Springer International Publishing, 2017 - P. Benner and M. Redmann,
*Approximation and Model Order Reduction for Second Order Systems with Lévy-Noise*, AIMS Proceedings, 2015 - P. Benner and M. Redmann,
*Model Reduction for Stochastic Systems*, Stochastic Partial Differential Equations: Analysis and Computations, 2015 - P. Benner, T. Damm, M. Redmann, and Y. R. Rodriguez Cruz,
, Linear Algebra and its Applications, 2014*Positive Operators and Stable Truncation* - P. Benner and M. Redmann,
, Proc. Appl. Math. Mech., 2013*Reachability and Observability**Concepts for Stochastic Systems*

## Talks

**Model Reduction for Stochastic Bilinear Systems;***International Congress on Industrial and Applied Mathematics*; Valencia; July 2019**Energy estimates and model order reduction for stochastic bilinear systems;***12th International Workshop on Stochastic Models and Control*; Cottbus; March 2019**Numerical approximations of parabolic rough PDEs;***Harmonic Analysis for Stochastic PDEs*; Delft; July 2018**Solving parabolic rough partial differential equations using regression;***13th International Conference in Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing*(invited talk); Rennes; July 2018**Numerical approximations of parabolic rough PDEs;***13th German Probability and Statistics Days*; Freiburg; March 2018**Beyond the theory of ordinary differential equations;***Seminar talk at the Department of Mathematics and Computer Science*(invited talk); Odense (Denmark); February 2018**Type II singular perturbation approximation for linear systems with Lévy noise;***EPSRC Durham Symposium on Model Order Reduction*(invited talk); Durham (UK); August 2017**A regression method to solve parabolic rough PDEs;***Ninth Workshop on Random Dynamical Systems*(invited talk); Bielefeld; June 2017**A regression method to solve parabolic rough PDEs;***7th Annual ERC Berlin-Oxford Young Researchers Meeting on Applied Stochastic Analysis*(invited talk); Berlin; May 2017**Model reduction for stochastic differential equations;***Stochastic Analysis Seminar in Oxford*(invited by Prof. Terry Lyons); Oxford; October 2016**Low Order Approximations to Linear SPDEs with Lévy Noise;***5th Annual ERC Berlin-Oxford Young Researchers Meeting on Applied Stochastic Analysis*(invited talk); Berlin; August 2016**Alternative Approaches to "Standard" Balanced Truncation for Linear Systems Driven by Lévy Noise;***CSC/NDS Workshop on Computational Methods for High-Dimensional Problems*; Schloss Ringberg (Tegernsee); May 2016**Model Order Reduction for Linear Controlled SDEs with Lévy Noise;***Joint DMV and GAMM Annual Meeting*; Braunschweig; March 2016**An Overview of Balancing Related Model Order Reduction for Systems with Lévy Noise;***12th German Probability and Statistics Days*; Bochum; March 2016**Model Order Reduction for Linear Controlled SDEs with Lévy Noise;***Numerical Analysis Seminar at the University of Bath*(invited by Dr. Melina Freitag); Bath; December 2015**Balancing Related Model Order Reduction Applied to Linear Controlled SPDEs with Lévy Noise;**; Halle; October 2015**Singular Perturbation Approximation Applied to SPDEs;***ENUMATH Conference*; Ankara; September 2015**Singular Perturbation Approximation (SPA) angewendet auf SPDEs;***Stochastic Analysis Seminar at the University of Halle*(invited by Prof. Wilfried Grecksch); Halle, Germany; May 2015**Singular Perturbation Approximation Applied to SPDEs;***Winter School on Stochastic Analysis of Spatially Extended Models*; Darmstadt; March 2015**Balancing Related Model Order Reduction Applied to SPDEs;***Seminar talk at the University of Warwick (invited by Prof. Andrew Stuart)*; Coventry; February 2015**Stochastic PDEs - Approximation and MOR;***10th AIMS Conference on Dynamical Systems, Differential Equations and Applications*; Madrid; July 25, 2014**Model Order Reduction for Stochastic Systems;***Seminar talk at the University of Kaiserslautern (invited by Prof. Tobias Damm)*; Kaiserslautern; March 2014**Model Order Reduction for Linear Stochastic Differential Equations with Lévy Noise;***11th German Probability and Statistics Days*; Ulm; March 4, 2014**Modellreduktion für lineare stochastische Evolutionsgleichungen mit Lévy-Rauschen;***Stochastic Analysis Seminar at the University of Halle*(invited by Prof. Wilfried Grecksch); Halle, Germany; November 28, 2013**Projektionsmethoden zur Lösung stochastischer Evolutionsgleichungen;***9th Workshop for Doctoral Students of the Probability and Statistics Group*; Göttingen, Germany; August 2, 2013**Balanced Truncation for Stochastic Linear Systems with Lévy Noise;***84th GAMM Annual Meeting;*Novi Sad, Serbia; March 21, 2013**Balanced Truncation for Stochastic Differential Equations with L****évy Noise;***Elgersburg Workshop, February 11 - 14, 2013*; Elgersburg, Germany; February 13, 2013