Dieses Bild zeigt Barth

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

Allmandring 5b
70569 Stuttgart
Germany
Room: 01.034

  1. 2018

    1. 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.
  2. 2017

    1. 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.
    2. A. Barth and A. Stein, “A study of elliptic partial differential equations with jump diffusion  coefficients,” 2017.
    3. 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.
  3. 2016

    1. A. Barth and A. Stein, “Approximation and simulation of infinite-dimensional Lévy processes,” 2016.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. K. Carlberg, L. Brencher, B. Haasdonk, and A. Barth, “Data-driven time parallelism via forecasting,” 2016.
  4. 2014

    1. A. Barth and S. Moreno-Bromberg, “Optimal risk and liquidity management with costly refinancing opportunities,” Insurance Math. Econom., vol. 57, pp. 31--45, 2014.
    2. 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.
  5. 2013

    1. 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.
    2. 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.
    3. 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.
  6. 2012

    1. 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.
    2. 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.
    3. 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.
  7. 2011

    1. 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.
    2. 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.
  8. 2010

    1. A. Barth, “A finite element method for martingale-driven stochastic partial  differential equations,” Commun. Stoch. Anal., vol. 4, no. 3, pp. 355--375, 2010.
  9. 2009

    1. A. Barth, “Stochastic Partial Differential Equations: Approximations  and Applications,” PhD dissertation, University of Oslo, CMA, 2009.
  10. 2006

    1. A. Barth, “Distribution of the First Rendezvous Time of Two Geometric  Brownian Motions,” Master thesis, University of Mannheim, 2006.

Current and previous lectures can be found here.

Supervision of highly qualified personnel

PhD theses:

  • 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
-08/2017

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
-12/2009

Ph.D. student in Mathematics at the Center of Mathematics for Applications, University of Oslo, Norway
Thesis: Stochastic Partial Differential Equations: Approximations and Applications
Supervisors: Prof. Dr. Fred Espen Benth, Center of Mathematics for Applications, University of Oslo, Norway
Prof. Dr. Jürgen Potthoff, University of Mannheim, Germany

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: Simulation of Lévy-type stochastic partial differential equations

2018 - 2019

Post-doctoral Project from RISC, funded by the MWK: Polynomial Chaos for Lévy fields

2016 - 2017

Doctorate Project from the SRC SimTech, funded by the DFG: Elliptic Equations with Lévy field coefficients

2014 - 2017

Doctorate Project from the Juniorprofessorship-Program Baden-Württemberg: New Methods for Weak Approximations of Stochastic Partial Differential Equations with Lévy-Noise

2014 - 2017

Doctorate Project from the SRC SimTech, funded by the DFG: Random field solutions of hyperbolic partial differential equations

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