Prof. Dr.

# Andrea Barth

Head of Group

Institute of Applied Analysis and Numerical Simulation

Research Group for Computational Methods for Uncertainty Quantification

## Contact

+49 711 685-60121

Email

Allmandring 5b

70569
Stuttgart

Germany

Room: 01.034

### 2018

- A. Barth and T. Stüwe, “Weak convergence of Galerkin approximations of stochastic partial differential equations driven by additive Lévy noise,”
*Math. Comput. Simulation*, vol. 143, pp. 215--225, 2018.

### 2017

- A. Barth and F. G. Fuchs, “Uncertainty quantification for linear hyperbolic equations with stochastic process or random field coefficients,”
*Appl. Numer. Math.*, vol. 121, pp. 38--51, 2017. - A. Barth and A. Stein, “A study of elliptic partial differential equations with jump diffusion coefficients,” 2017.
- A. Barth, B. Harrach, N. Hyvönen, and L. Mustonen, “Detecting stochastic inclusions in electrical impedance tomography,”
*Inv. Prob.*, vol. 33, no. 11, p. 115012, 2017.

### 2016

- A. Barth and A. Stein, “Approximation and simulation of infinite-dimensional Lévy processes,” 2016.
- A. Barth, C. Schwab, and J. Sukys, “Multilevel Monte Carlo simulation of statistical solutions to the Navier-Stokes equations,” in
*Monte Carlo and quasi-Monte Carlo methods*, vol. 163, Springer, Cham, 2016, pp. 209--227. - A. Barth and I. Kröker, “Finite volume methods for hyperbolic partial differential equations with spatial noise,” in
*Springer Proceedings in Mathematics and Statistics*, vol. submitted, Springer International Publishing, 2016. - A. Barth and F. G. Fuchs, “Uncertainty quantification for hyperbolic conservation laws with flux coefficients given by spatiotemporal random fields,”
*SIAM J. Sci. Comput.*, vol. 38, no. 4, pp. A2209--A2231, 2016. - A. Barth, S. Moreno-Bromberg, and O. Reichmann, “A Non-stationary Model of Dividend Distribution in a Stochastic Interest-Rate Setting,”
*Comp. Economics*, vol. 47, no. 3, pp. 447--472, 2016. - K. Carlberg, L. Brencher, B. Haasdonk, and A. Barth, “Data-driven time parallelism via forecasting,” 2016.

### 2014

- A. Barth and S. Moreno-Bromberg, “Optimal risk and liquidity management with costly refinancing opportunities,”
*Insurance Math. Econom.*, vol. 57, pp. 31--45, 2014. - A. Barth and F. E. Benth, “The forward dynamics in energy markets -- infinite-dimensional modelling and simulation,”
*Stochastics*, vol. 86, no. 6, pp. 932--966, 2014.

### 2013

- A. Abdulle, A. Barth, and C. Schwab, “Multilevel Monte Carlo methods for stochastic elliptic multiscale PDEs,”
*Multiscale Model. Simul.*, vol. 11, no. 4, pp. 1033--1070, 2013. - A. Barth, A. Lang, and C. Schwab, “Multilevel Monte Carlo method for parabolic stochastic partial differential equations,”
*BIT*, vol. 53, no. 1, pp. 3--27, 2013. - A. Barth and A. Lang, “L^p and almost sure convergence of a Milstein scheme for stochastic partial differential equations,”
*Stochastic Process. Appl.*, vol. 123, no. 5, pp. 1563--1587, 2013.

### 2012

- A. Barth and A. Lang, “Simulation of stochastic partial differential equations using finite element methods,”
*Stochastics*, vol. 84, no. 2–3, pp. 217--231, 2012. - A. Barth and A. Lang, “Milstein approximation for advection-diffusion equations driven by multiplicative noncontinuous martingale noises,”
*Appl. Math. Optim.*, vol. 66, no. 3, pp. 387--413, 2012. - A. Barth and A. Lang, “Multilevel Monte Carlo method with applications to stochastic partial differential equations,”
*Int. J. Comput. Math.*, vol. 89, no. 18, pp. 2479--2498, 2012.

### 2011

- A. Barth, C. Schwab, and N. Zollinger, “Multi-level Monte Carlo finite element method for elliptic PDEs with stochastic coefficients,”
*Numer. Math.*, vol. 119, no. 1, pp. 123--161, 2011. - A. Barth, F. E. Benth, and J. Potthoff, “Hedging of spatial temperature risk with market-traded futures,”
*Appl. Math. Finance*, vol. 18, no. 2, pp. 93--117, 2011.

### 2010

- A. Barth, “A finite element method for martingale-driven stochastic partial differential equations,”
*Commun. Stoch. Anal.*, vol. 4, no. 3, pp. 355--375, 2010.

### 2009

- A. Barth, “Stochastic Partial Differential Equations: Approximations and Applications,” University of Oslo, CMA, 2009.

### 2006

- A. Barth, “Distribution of the First Rendezvous Time of Two Geometric Brownian Motions,” 2006.

**Current and previous lectures can be found ****here**.

**Supervision of highly qualified personnel**

**PhD theses:**

- R. Merkle: Analysis and Simulation of Lévy Random Fields, since April 2019
- L. Brencher: Analysis of Stochastic Partial Differential Equations and their efficient Simulation, since October 2018
- A. Stein: Approximations of Stochastic Partial Differential Equations with Lévy-Noise, since April 2016

**Master theses:**

- C. Grüner: Novel numerical methods in quantitative finance, 2019
- F. Altmann: Finite Element Approximations of Random Fields, 2019
- A. Baransegata: Optimal error rates for multilevel Monte Carlo methods, 2019
- S. Klumpp: Optimal sampling in multilevel Monte Carlo methods, 2019
- R. Merkle: Weak convergence of Lévy-driven stochastic partial differential equations, 2019
- L. Brencher: Time-parallel multilevel Monte Carlo methods, 2018
- T. Cataltepe: Statistical modeling of the system bounds for position estimation in highly automated driving, 2018 (in cooperation with the DAIMLER AG)
- J. Abendschein: Density estimation with Multilevel Monte Carlo methods, 2018
- S. Daas: Optimal dividend distribution under stochastic re-financing costs, 2017
- B. Sunjic: Multilevel Monte Carlo methods of Wong-Zakai Approximations, 2017
- S. Herrmann: Multilevel Monte Carlo Methods and Wong-Zakai Approximations, 2016
- G. Prestipino: Numerical Methods for Parabolic PDEs with Time-dependent Random-field-coeffiffcients, 2015
- Y. E. Poltera: Multilevel Monte Carlo Finite Difference Method for Statistical Solutions to the Navier-Stokes Equations, 2013
- N. Zollinger: Multi-Level Monte Carlo Finite Element Method for Elliptic Partial Differential Equations with Stochastic Data, 2010

**Bachelor theses:**

- V. Krasniqi: On generalized central limit theorems, 2019
- A. Gross: Optimal dividend distribution under stochastic refinancing possibilities, 2017
- P. Oduro: First exit-time problems and multilevel Monte Carlo methods, 2017
- A. Wörner: Uncertainty Quantification for electric motors, 2017 (in cooperation with the BOSCH)
- L. Eisert: Simulationen zur gepulsten Laserbestrahlung für die Beseitigung von Weltraumschrott, 2017 (in cooperation with the DLR)
- V. Scheffold: Review on dividend distribution models, 2016
- B. Sunjic: Optimal dividend distribution in bond-financed models, 2016
- P. Schroth: Approximation and Simulation of infinite dimensional Lévy-processes, 2016
- L. Brencher: Leveraging spatial and temporal data for time-parallel model reduction, 2015
- V. Mohan: Discontinuous Galerkin methods for hyperbolic stochastic partial differential equations, 2012

**Semester projects:**

- P. Horn: Mortar FEM methods for elliptic equations containing discontinuous random coefficients, 2018
- L. de Vries: Quantifying uncertainty in Richards' equation, 2018
- T. Brünette: Wong-Zakai approximations for first hitting time problems, 2017
- C. Proissl: Optimal Markov Chain Monte Carlo methods for non-Gaussian random fields, 2017
- M. Schmidgall: Uncertainty quantification with multi-resolution and multi-wavelet discretisations, 2017
- L. Mauch: Modeling of groundwater flow with elliptic equations containing discontinuous random coefficients, 2017
- N. Wildt: Optimized multilevel Monte Carlo methods for Particle-Tracking Random Walk simulations, 2016
- C. Michalkowski: Multilevel Monte Carlo methods for Particle-Tracking Random Walk simulations for advective-dispersive transport through porous media, 2014

since 08/2017 |
W3-Professor for Computational Methods for Uncertainty Quantification at the Excellence Cluster for Simulation Technology, IANS, University of Stuttgart, Germany |

12/2013 |
Juniorprofessor at the Excellence Cluster for Simulation Technology, University of Stuttgart, Germany |

01/2010 - 11/2013 |
Lecturer and postdoctoral researcher at the Seminar for Applied Mathematics, ETH Zürich, Switzerland |

09/2006 |
Ph.D. student in Mathematics at the Center of Mathematics for Applications, University of Oslo, Norway |

2019 - 2025 |
Principal Investigator: ExC 2075 "Data-Integrated Simulation Science" |

2019 - 2023 |
Principal Investigator: SFB/TRR 161 "Quantitative Methods for Visual Computing" |

2018 - 2021 |
Doctorate Project from the SC SimTech (ExC 310 / ExC 2075), funded by the DFG: |

2018 - 2019 |
Post-doctoral Project from RISC, funded by the MWK: |

2016 - 2017 |
Doctorate Project from the SRC SimTech, funded by the DFG: |

2014 - 2017 |
Doctorate Project from the Juniorprofessorship-Program Baden-Württemberg: |

2014 - 2017 |
Doctorate Project from the SRC SimTech, funded by the DFG: |

Computational and Applied Mathematics Seminar, Chalmers, Gothenburg, Sweden, September 12th, 2018*On random elliptic problems with jump-diffusion coefficients*Zürich Summer School, ETH Zürich, Zürich, Switzerland, August 27th - August 31st, 2018*Introduction to (multilevel) Monte Carlo methods*Workshop in honor of Jürgen Potthoff, University of Mannheim, Mannheim, Germany, June 22nd, 2018*Approximation and Simulation of infinite-dimensional Lévy-SPDEs*SPA, Chalmers, Gothenburg, Sweden, June 11th - June 15th, 2018*Approximation and Simulation of infinite-dimensional Lévy-SPDEs*EWM, University of Heidelberg, Heidelberg, Germany, May 18th - May 19th, 2018*Introduction to Uncertainty Quantification*46th SpeedUp Workshop on "UQ and HPC", University of Bern, Bern, Switzerland, September 1st, 2017*Quantication of Uncertainty via multilevel Monte Carlo Methods*Stochastic (Partial) Differential Equations Day, TU Munich, Munich, Germany, June 26th, 2017*Approximations of Stochastic Partial Differential Equations with Lévy noise*NASPDE 2017, JKU Linz, Linz, Austria, June 22nd, 2017*Simulation of infinite-dimensional Lévy processes*Mathematics Colloquium, Johannes Gutenberg University of Mainz, Mainz, Germany, May 18th, 2017*Quantification of Uncertainty via multilevel Monte Carlo Methods*School on Uncertainty*Stochastic Partial Differential Equations and infinite dimensional Lévy fields**Quantification for Hyperbolic Equations*, GSSI, L'Aquila, Italy, April 24th - April 28th, 2017Workshop: Stochastic Differential Equations, Oberwolfach, Germany, February 5th - February 10th, 2017*Simulating infinite dimensional Lévy fields*Mathematics Colloquium, University of Oldenburg, Germany, December 1st, 2016*Simulating infinite dimensional Lévy fields*Nonlinear Stochastic Evolution Equations, TU Berlin, Germany, November 3rd - November 5th, 2016*Simulating infinite dimensional Lévy fields*Mini-course at the international Symposium on Analysis and Applications, Metepec Atlixco, Puebla, Mexico, September 7th - September 10th, 2016*Multilevel Monte Carlo methods*SIAM UQ, EPF Lausanne, Switzerland, April 5th - April 8th, 2016*Optimizing a multilevel Monte Carlo method*DMV and GAMM Annual Meeting, University of Braunschweig, Germany, March 7th - March 11th, 2016*Multilevel Monte Carlo methods for stochastic multiscale problems*German Probability and Statistics Days, University Bochum, Germany, March 1st - March 4th, 2016*A structural model of an insurance firm*; Winterschool on Uncertainty Quantification, wesNum, Bern, Switzerland, February 18th - February 21st, 2016*Approximations of stochastic partial differential equations and applications in forward market*sMinicourse at the Winterschool on Uncertainty Quantification, wesNum, Bern, Switzerland, February 18th - February 21st, 2016*Introduction to (multilevel) Monte Carlo methods*Mathematical Colloquium, University of Ulm, Germany, January 22nd, 2016*Multilevel Monte Carlo methods for stochastic multiscale problems*Seminar in Numerical Analysis, University of Basel, Switzerland, October 9th, 2015*Multilevel Monte Carlo methods for stochastic multiscale problems*MCM2015, JKU, Linz, Austria, July 6th - July 10th, 2015*Multilevel Monte Carlo approximation of statistical solutions to the Navier-Stokes equations*Advances in Numerical Methods for SPDEs, Institut Mittag-Leffler, Stockholm, Sweden, June 16th - June 18th, 2015*Multilevel Monte Carlo approximation of statistical solutions to the Navier-Stokes equations*Probability Seminar, University Duisburg-Essen, Germany, June 9th, 2015*Galerkin approximations for stochastic partial differential equations*Seminar in Numerical Analysis, University Tübingen, Germany, February 12th, 2015*Approximations of first order stochastic partial differential equations and applications in forward markets*Mathematisches Seminar, RWTH Aachen, Germany, February 9th, 2015*Introduction to multilevel Monte Carlo methods for stochastic partial differential equations*Research Seminar on Stochastic Analysis and Financial Markets, HU Berlin, Germany, December 4th, 2014*Approximations of stochastic partial differential equations and applications in forward markets*Mathematisches Seminar, University of Vienna, Austria, October 14th, 2014*Stochastic Partial Differential Equations: An Introduction*NASPDE 2014, EPF Lausanne, Switzerland, September 9th - September 10th, 2014*Modeling with Stochastic Partial Differential Equations*RDSN 2014, University of Mannheim, Germany, June 25th - June 27th, 2014*Hyperbolic Stochastic Partial Differential Equations and Energy Markets*MCQMC 2014, KU Leuven, Belgium, April 6th - April 11th, 2014*Multilevel Monte Carlo methods for elliptic equations*School of Business Informatics and Mathematics, University of Mannheim, Germany, December 9th, 2013*Multilevel Monte Carlo methods and Stochastic Partial Differential Equations*SimTech JP Colloquium, University Stuttgart, Germany, June 24th, 2013*Multilevel Monte Carlo methods*Institute for Mathematics, TU Darmstadt, Germany, June 17th, 2013*Multilevel Monte Carlo methods*Institute for Mathematics, University Augsburg, Germany, May 27th, 2013*Multilevel Monte Carlo methods*IWR, University Heidelberg, Germany, December 10th, 2012*A multilevel Monte Carlo method for stochastic, elliptic partial differential equations*Institute for Numerical Simulation, University Bonn, Germany, November 13th, 2012*A multilevel Monte Carlo method for stochastic, elliptic partial differential equations*24th Biennial Conference on Numerical Analysis, Glasgow, Great Britain, June 28th – July 1st, 2011*MLMC-FE method for elliptic PDEs with stochastic coefficients*Research seminar on hyperbolic PDEs, Zurich, Switzerland, October 25th, 2010*Modeling forward dynamics in energy markets with hyperbolic SPDEs*SCAIM (Seminar for Computational, Applied and Industrial Mathematics) Vancouver, BC, Canada, June 22nd, 2010*MLMC-FE method for elliptic PDEs with stochastic coefficients*Weather derivatives and Risk, Berlin, Germany, January 27th - January 28th, 2010*Forward dynamics in energy markets - An infinite dimensional approach*Oberseminar Finanz- und Versicherungsmathematik LMU - TUM, Munich, Germany, November 12th, 2009*Finite Element Method for Stochastic Partial Differential Equations and Applications*International Conference on Stochastic Analysis and Applications, Hammamet, Tunesia, October 12th - October 17th, 2009*Modeling of Energy Forwards: An infinite dimensional approach*Seminar for Applied Mathematics, ETH Zürich, Zürich, Switzerland, August 13th, 2009*Finite Element method for SPDEs driven by Lévy noise*33rd Conference on Stochastic Processes and Their Applications, Berlin, Germany, July 27th - July 31st, 2009*FEM for martingale-driven SPDE's*Probability and Statistics Seminar, WSU, Detroit, USA, May 13th, 2009*FEM for Hilbert-space-valued SDE's driven by Lévy noise*Seminario de Probabilidad, Departamento de Matemáticas, UNAM, Mexico City, Mexico, April 14th, 2009*FEM for Hilbert-space-valued SDE's driven by Lévy noise*Probability Seminar, CIMAT, Guanajuato, Mexico, April 15th - April 16th, 2009*FEM for Hilbert-space-valued SDE's driven by Lévy noise*5th World Congress of the Bachelier Finance Society, London, Great Britain, July 15th - July 19th, 2008*Hedging of spatial temperature risk with market-traded futures*Workshop on Recent Developments in Financial Mathematics and Stochastic Calculus, Ankara, Turkey, April 23rd – April 26th, 2008*Simulation of Random Fields*Innovations in Mathematical Finance, Loen, Norway, June 25th - July 1st, 2007**Spatial Temperature Risk: Hedging and Simulation**Mathematics and the Environment, Banff, Canada, May 8th - May 13th, 2007*Spatial Temperature Risk: Hedging and Simulation*SAMSA 2006, Gaborone, Botswana, November 27th - December 1st, 2006*Hedging temperature risk with synthetic temperature futures*