AG Funktionalanalysis und stochastische Analysis

Prof. Dr. Martin Grothaus

Anschrift

Gottlieb-Daimler-Straße
Gebäude: 48
Raum: 626
67663 Kaiserslautern

Postfach: 3049
67653 Kaiserslautern

Kontakt

Tel.: +49 631 205 4591

Fax: +49 631 205 4738

E-Mail: grothaus@mathematik.uni-kl.de

Lebenslauf

2010
  • Verleihung des Lehrpreises Rheinland-Pfalz
2008
  • Professor (W3) für Funktionalanalysis an der Technischen Universität Kaiserslautern
  • Ruf auf die W3-Professur für Funktionalanalysis an der Technischen Universität Kaiserslautern
  • Ruf auf die W3-Professur für Stochastik an der Philipps-Universität Marburg
  • Ruf auf die Universitätsprofessur für Wahrscheinlichkeitstheorie und Statistik an der Universität Innsbruck
2005
  • Positive Evaluierung als Juniorprofessor
2002–2008
  • Juniorprofessor für Funktionalanalysis an der Technischen Universität Kaiserslautern
2002
  • wissenschaftlicher Mitarbeiter an der Universität Bonn und der Universität Bielefeld
2001–2002
  • Humboldt-Stipendiat an der Cornell University
2000
  • Verleihung eines Humboldt-Stipendiums
1999–2001
  • wissenschaftlicher Mitarbeiter an der Universität Bonn
1998
  • Erwerb des Titels Dr. rer. nat., Universität Bielefeld, Betreuer: L. Streit und Yu. G. Kondratiev
1996–1998
  • wissenschaftlicher Mitarbeiter an der Universität Bielefeld
1996
  • Erwerb des Diploms in Mathematik, Universität Bielefeld, Betreuer: Yu. G. Kondratiev
  • Erwerb des Diploms in Physik, Universität Bielefeld, Betreuer: L. Streit

Forschungsinteressen

  • Funktionalanalysis (Operator-Halbgruppen, Dirichlet-Formen)
  • Stochastische Analysis (Konstruktion, Ergodizität und Skalierungslimiten von stochastischen Dynamiken)
  • White Noise Analysis
  • Mathematische Physik (Statistische Mechanik, Quantenmechanik, Quantenfeldtheorie, Polymer-Modelle)

Publikationen

  1. Bernido, Christopher C. (ed.); Carpio-Bernido, Maria Victoria (ed.); Grothaus, Martin (ed.); Kuna, Tobias (ed.); Oliveira, Maria João (ed.); da Silva, José Luís (ed.) (2016). Stochastic and infinite dimensional analysis. 300 p. Birkhäuser/Springer, Basel: 978-3-319-07244-9
  2. Eberle, A., Grothaus, M., Hoh, W., Kassmann, M., Stannat, W., Trutnau, G. (Eds.) (2018). Stochastic Partial Differential Equations and Related Fields. 229, 574. (In Honor of Michael Röckner SPDERF, Bielefeld, Germany, October 10 -14, 2016), Springer International Publishing: 978-3-319-74928-0
  1. M. Grothaus; S. Wittmann (2024). Mosco Convergence of Gradient Forms with Non-Convex Interaction Potential. Integral Equations and Operator Theory, 96, 29, https://doi.org/10.1007/s00020-024-02775-6
  2. M. Grothaus; P. Ren; F.-Y. Wang (2024). Singular degenerate SDEs: Well-posedness and exponential ergodicity. Journal of Differential Equations, 413, 632-661. https://authors.elsevier.com/a/1jjGa50j-zRTv
  3. B. Eisenhuth; M. Grothaus (2023). Hypocoercivity for non-linear infinite-dimensional degenerate stochastic differential equations. Stochastics and Partial Differential Equations: Analysis and Computations. https://link.springer.com/article/10.1007/s40072-023-00299-5 
  4. W. Bock;  M. Grothaus; K. Orge (2023). Stochastic Analysis for Vector-Valued Generalized Grey Brownian Motion. Theory of Probability and Mathematical Statistics, 108, 1-27. https://doi.org/10.1090/tpms/1184 
  5. A. Bertram; M. Grothaus (2023). Convergence rate for degenerate partial and stochastic differential equations via weak Poincaré inequalities. Journal of Differential Equations. https://doi.org/10.1016/j.jde.2023.03.039  50 days' free access
  6. M. Grothaus; H. Pribawanto Suryawan; J. L. da Silva (2023). A white noise approach to stochastic currents of Brownian motion. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 26, (1). Article No. 2250025. https://dx.doi.org/10.1142/S0219025722500254
  7. M. Grothaus; M. Sauerbrey (2023). Dirichlet form analysis of the Jacobi process. Stochastic Processes and their Applications, 157, 376-412. https://authors.elsevier.com/a/1gJ3s15DqVIb2d  
  8. B. Eisenhuth; M. Grothaus (2022). Essential m-dissipativity for possibly degenerate generators of infinite-dimensional diffusion processes. Integral Equations and Operator Theory. 94, (28). https://doi.org/10.1007/s00020-022-02707-2
  9. A. Bertram; M. Grothaus (2022). Essential m-dissipativity and hypocoercivity of Langevin dynamics with multiplicative noise. Journal of Evolution Equations. 22, (11). https://doi.org/10.1007/s00028-022-00773-y
  10. M. Grothaus; M. Mertin (2022). Hypocoercivity of Langevin-type dynamics on abstract smooth manifolds. Stochastic Processes and their Applications, 146, 22-59. https://authors.elsevier.com/c/1eOw615DqVEmnw 
  11. M. Grothaus; J. Müller; A. Nonnenmacher (2022). An improved characterisation of regular generalised functions of white noise and an application to singular SPDEs. Stochastics and Partial DifferentialEquations: Analysis and Computations, 10, 359–391. https://doi.org/10.1007/s40072-021-00200-2 und https://rdcu.be/cxbqE
  12. M. Grothaus; A. Nonnenmacher (2020). Overdamped limit of generalized stochastic Hamiltonian systems for singular interaction potentials. Journal of Evolution Equations. 20, 577–605. https://doi.org/10.1007/s00028-019-00530-8
  13.  M. Grothaus; F.-Y. Wang (2019). Weak Poincaré Inequalities for Convergence Rate of Degenerate Diffusion Processes.  Annals of Probability, 47, (5), 2930-2952. http://dx.doi.org/10.1214/18-AOP1328
  14. M. Grothaus and R. Voßhall (2018). Strong Feller property of sticky reflected distorted Brownian motion. Journal of Theoretical Probability. 31, (2), 827-852.
  15. M. Grothaus; R. Voßhall (2018). Integration by parts on the law of the modulus of the Brownian bridge. Stochastics and Partial Differential Equations: Analysis and Computations. 6, (3), 335-363.
  16. M. Grothaus; R. Voßhall (2017). Stochastic differential equations with sticky reflection and boundary diffusion. Electronic Journal of Probability. 22, (7), 37 pp.
  17. M. Grothaus; Felix Riemann (2017). A fundamental solution to the Schrödinger equation with Doss potentials and its smoothness. Journal of Mathematical Physics. 58, (5), 25 pp.
  18. B. Baur, M. Grothaus (2017). Skorokhod decomposition for a reflected Lp-strong Feller diffusion with singular drift. Stochastics. 90, (4), 539-568.
  19. T. Fattler; M. Grothaus; R. Voßhall (2016). Construction and analysis of a sticky reflected distorted Brownian motion. Annales de l'Institut Henri Poincaré. 52, (2), 735-762.
  20. M. Grothaus; N. Marheineke (2016). On a nonlinear partial differential algebraic system arising in the technical textile industry: analysis and numerics. IMA Journal of Numerical Analysis. 36, (4), 1783-1803.
  21. M. Grothaus; F. Jahnert (2016). Mittag-Leffler analysis II: Application to the fractional heat equation. Journal of Functional Analysis. 270, (7), 2732-2768.
  22. Butko, Y.A.; Grothaus, M., Smolyanov, O.G. (2016). Feynman formulae and phase space Feynman path integrals for tau-quantization of some Lévy-Khintchine type Hamilton functions. Journal of Mathematical Physics. 57, (2), 023508, 22 pp.
  23. M. Grothaus; P. Stilgenbauer (2016). Hilbert space hypocoercivity for the Langevin dynamics revisited. Methods of Functional Analysis and Topology. 22, (2), 152-168.
  24. M. Grothaus; F. Jahnert; F. Riemann; J. L. da Silva (2015). Mittag-Leffler analysis I: Construction and characterization. Journal of Functional Analysis. 268, (7), 1876-1903.
  25. W. Bock; M. Grothaus (2015). The Hamiltonian path integrand for the charged particle in a constant magnetic field as white noise distribution. Infinite Dimensional Analysis, Quantum Probability and Related Topics. 18, (2), 1550010, 22 pp.
  26. M. Grothaus; P. Stilgenbauer (2015). A hypocoercivity related ergodicity method for singularly distorted non-symmetric diffusions. Integral Equations and Operator Theory. 83, (3), 331-379.
  27. B. Baur; M. Grothaus (2014). Construction and strong Feller property of distorted elliptic diffusion with reflecting boundary. Potential Analysis. 40, (4), 391-425.
  28. M. Grothaus; F. Riemann; H. P. Suryawan (2014). A White Noise approach to the Feynman integrand for electrons in random media. Journal of Mathematical Physics. 55, (1), 013507, 16 pp.
  29. M. Grothaus; A. Klar; J. Maringer; P. Stilgenbauer; R. Wegener (2014). Application of a three-dimensional fiber lay-down model to non-woven production processes. Journal of Mathematics in Industry. 14, (4), Art. 4, 19 pp.
  30. M. Grothaus; P. Stilgenbauer (2014). Hypocoercivity for Kolmogorov backward evolution equations and applications. Journal of Functional Analysis. 267, (10), 3515-3556.
  31. Bock, W.; Götz, T.; Grothaus, M.; Liyanage, U.P. (2014). Parameter estimation from occupation times-a white noise approach. Communications on Stochastic Analysis. 8, (4), 489-499.
  32. F. Conrad; T. Fattler; M. Grothaus (2013). An invariance principle for the tagged particle process in continuum with singular interaction potential. Infinite Dimensional Analysis, Quantum Probability and Related Topics. 16, (4), 1350032, 37 pp.
  33. B. Baur; M. Grothaus; P. Stilgenbauer (2013). Construction of -strong Feller Processes via Dirichlet Forms and Applications to Elliptic Diffusions. Potential Analysis. 38, (4), 1233-1258.
  34. M. Grothaus; P. Stilgenbauer (2013). Geometric Langevin equations on submanifolds and applications to the stochastic melt-spinning process of nonwovens and biology. Stochastics and Dynamics. 13, (4), 135001, 34 pp.
  35. B. Baur; M. Grothaus; Mai T. T. (2013). Analytically weak solutions to linear SPDEs with unbounded time-dependent differential operators and an application. Communications on Stochastic Analysis. 7, (4), 551-571.
  36. M. Grothaus; L. Streit; A. Vogel (2012). The complex scaled Feynman-Kac formula for singular initial distributions. Stochastics. 84, (2-3), 347-366.
  37. B. Baur; F. Conrad; M. Grothaus (2012). Smooth contractive embeddings and application to Feynman formula for parabolic equations on smooth bounded domains. Communications in Statistics - Theory and Methods. 40, (19-20), 3452-3464.
  38. F. Conrad; M. Grothaus; J. Lierl; O. Wittich (2012). Convergence of Brownian motion with a scaled Dirac Delta potential. Proceedings of the Edinburgh Mathematical Society. 55, (2), 403-427.
  39. W. Bock; M. Grothaus (2012). White noise approach to phase space Feynman path integrals. Theory Probab. Math. Stat.. 85, 7-22.
  40. W. Bock; M. Grothaus; S. Jung (2012). The Feynman integrand for the charged particle in a constant magnetic field as White Noise distribution. Communications in Stochastic Analysis. 6, (4), 649-668.
  41. F. Conrad; M. Grothaus (2011). N/V-limit for Langevin dynamics in continuum. Reviews in Mathematical Physics. 23, (1), 1-51.
  42. T. Fattler; M. Grothaus (2011). Tagged particle process in continuum with singular interactions. Infinite Dimensional Analysis, Quantum Probability and Related Topics. 14, (1), 105-136.
  43. M. Grothaus; M. J. Oliveira; J. L. da Silva; L. Streit (2011). Self-avoiding fractional Brownian motion - The Edwards model. Journal of Statistical Physics. 145, (6), 1513-1523.
  44. F. Conrad; M. Grothaus (2010). Construction, ergodicity and rate of convergence of N-particle Langevin dynamics with singular potentials. Journal of Evolution Equations. 10, (3), 623-662.
  45. Y. A. Butko; M. Grothaus; O. G. Smolyanov (2010). Lagrangian Feynman formulae for second order parabolic equations in bounded and unbounded domains. Infinite Dimensional Analysis, Quantum Probability and Related Topics. 13, (3), 377-392.
  46. M. Grothaus; T. Raskop (2010). Limit formulae and jump relations of potential theory in Sobolev spaces. GEM: International Journal on Geomathematics. 1, (1), 51-100.
  47. M. Grothaus; T. Raskop (2009). The outer oblique boundary problem of potential theory. Numerical Functional Analysis and Optimization. 30, (7-8), 711-750.
  48. M. Grothaus; L. Streit; A. Vogel (2009). Feynman integrals as Hida distributions: the case of non-perturbative potentials. SMF, Astérisque. 327, 55-68. (Dai, Xianzhe(ed.) et al., From probability to geometry I. Festschrift in honor of the 60th birthday of Jean-Michel Bismutth)
  49. T. Fattler; M. Grothaus (2008). Construction of elliptic diffusions with reflecting boundary condition and an application to continuous N-particle systems with singular interactions. Proceedings of the Edinburgh Mathematical Society. Series II.. 51, (2), 337-362.
  50. Y. A. Butko; M. Grothaus; O. G. Smolyanov (2008). Feynman formula for a class of second order parabolic equations in a bounded domain. Doklady Mathematics. 78, (1), 1-6.
  51. M. Grothaus; A. Klar (2008). Ergodicity and rate of convergence for a non-sectorial fiber lay-down process. SIAM Journal on Mathematical Analysis. 40, (3), 968-983.
  52. F. Conrad; M.Grothaus (2008). Construction of N-particle Langevin dynamics for -potentials via generalized Dirichlet forms. Potential Analysis. 28, (3), 261-282.
  53. T. Fattler; M. Grothaus (2007). Strong Feller properties for distorted Brownian motion with reflecting boundary condition and an application to continuous N-particle systems with singular interactions. Journal of Functional Analysis. 246, (2), 217-241.
  54. Yu.G. Kondratiev; M. Grothaus; M. Röckner (2007). N/V-limit for stochastic dynamics in continuous particle systems. Probability Theory and Related Fields. 137, 121-160.
  55. M. Grothaus (2006). Scaling limit of fluctuations for the equilibrium Glauber dynamics in continuum. Journal of Functional Analysis. 239, (2), 414-445.
  56. M. Grothaus; T. Raskop (2006). On the oblique boundary problem with a stochastic inhomogeneity. Stochastics. 78, (4), 233-257.
  57. M. Grothaus; L. Gross (2005). Reverse hypercontractivity for subharmonic functions. Canadian Journal of Mathematics. 57, (3), 506-534.
  58. M. Grothaus; Yu.G. Kondratiev; E. Lytvynov; M. Röckner (2003). Scaling limit of stochastic dynamics in classical continuous systems. Annals of Probability. 31, (3), 1494-1532.
  59. S. Albeverio; M. Grothaus; Yu.G. Kondratiev; M. Röckner (2001). Stochastic dynamics of fluctuations in classical continuous systems. Journal of Functional Analysis. 185, (1), 129-154.
  60. M. Grothaus; L. Streit (2000). On regular generalized functions in white noise analysis and their applications. Methods of Functional Analysis and Topology. 6, (1), 14-27.
  61. M. Grothaus; Yu.G. Kondratiev; L. Streit (2000). Scaling limits for the solution of Wick type Burgers equation. Random Operators and Stochastic Equations. 8, (1), 1-26.
  62. M. Grothaus; L. Streit; I.V. Volovich (1999). Knots, Feynman diagrams and matrix models. Infinite Dimensional Analysis, Quantum Probability and Related Topics. 2, (3), 359-380.
  63. M. Grothaus; L. Streit (1999). Quadratic actions, semi-classical approximation, and delta sequences in Gaussian analysis. Reports on Mathematical Physics. 44, (3), 381-405.
  64. M. Grothaus; L. Streit (1999). Construction of relativistic quantum fields in the framework of white noise analysis. Journal of Mathematical Physics. 40, (11), 5387-5405.
  65. M. Grothaus; Yu.G. Kondratiev; G.F. Us (1999). Wick calculus for regular generalized stochastic functions. Random Operators and Stochastic Equations. 7, (3), 301-328.
  66. M. Grothaus; Yu.G. Kondratiev; L. Streit (1999). Regular generalized functions in Gaussian analysis. Infinite Dimensional Analysis, Quantum Probability and Related Topics. 2, (1), 1-25.
  67. M. Grothaus; D.C. Khandekar; J.L. Silva; L. Streit (1997). The Feynman integral for time dependent anharmonic oscillators. Journal of Mathematical Physics. 38, (6), 3278-3299.
  68. M. Grothaus; Yu.G. Kondratiev; L. Streit (1997). Complex Gaussian analysis and the Bargmann-Segal space. Methods of Functional Analysis and Topology. 3, (2), 46-64.
  1. M. Grothaus; M. Mertin; P. Stilgenbauer (2018). Hypocoercivity for geometric Langevin equations motivated by fibre lay-down models arising in industrial application. GAMM - Mitteilungen. 2018;41:e201800011, https://doi.org/10.1002/gamm.201800011
  2. M. Grothaus; P. Stilgenbauer (2014). Hypocoercivity for degenerate Kolmogorov equations and applications to the Langevin dynamics. P. Steinmann and G. Leugering (eds.) Special Issue: 85th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Erlangen 2014. 999-1000.
  3. M. Grothaus; P. Stilgenbauer (2014). A hypocoercivity related ergodicity method for Kolmogorov equations. P. Steinmann and G. Leugering (eds.) Special Issue: 85th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Erlangen 2014. 1009-1010.
  4. M. Grothaus; A. Klar; J. Maringer; P. Stilgenbauer (2012). The Analysis of stochastic fiber lay-down models: Geometry and convergence to equilibrium of the basic model. Proceedings in Applied Mathematics and Mechanics, Vol. 12. 611-612.
  5. M. Grothaus; T. Raskop (2010). Oblique Stochastic Boundary-Value Problem. Handbook of Geomathematics. Willi Freeden et al. (eds.) 1049-1076.
  6. M. Grothaus; A. Vogel (2008). The Feynman integrand as a white noise distribution beyond perturbation theory. Stochastics and quantum dynamics in biomolecular systems. Bernido, Christopher C. et al. (eds.) 25-33.
  7. M. Grothaus (2004). Dirichlet Forms and (Stochastic) Partial Differential Equations. Oberwolfach Reports, 1(2). 1431-1432.