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“He who seeks for methods without having a definite problem in mind seeks for the most part in vain.”

David Hilbert

Webpage last updated April 30, 2023

  • Stochastic dynamics and stochastic partial differential equations
  • (Stochastic) variational calculus and infinite dimensional optimization
  • Time-evolution models from biology, ecology and neuroscience involving randomness
  • Singular phenomena, mathematical perturbation theory and modeling of critical physical systems
  • Asymptotic invariance properties, ergodicity and uniqueness questions of complex stochastic systems
  • Theoretical approximation theory and variational convergence

Submitted for peer review

    1. J. M. Tölle (with E. Hausenblas). The stochastic Klausmeier system and a stochastic Schauder-Tychonoff type theorem. Preprint, submitted (2023), 60 pp., arXiv:1912.00996.
    2. J. M. Tölle (with F. Seib and W. Stannat). Stability and moment estimates for the stochastic singular Φ-Laplace equation. Preprint, submitted (2022), 24 pp., arXiv:2103.03194.

Accepted for journal publication

    1. J. M. Tölle (with D. Blömker). Singular limits for stochastic equations. To appear in Stochastics and Dynamics (2023+), 24 pp., arXiv:2204.09545.
    2. J. M. Tölle (with M. Hinz and L. Viitasaari). Variability of paths and differential equations with BV-coefficients. To appear in Annales de l’Institut Henri Poincaré (B) – Probabilités et Statistiques (2022+), 46 pp., arXiv:2003.11698.

Journal Publications

Published in peer reviewed proceedings

    1. J. M. Tölle. Estimates for nonlinear stochastic partial differential equations with gradient noise via Dirichlet forms. In: Eberle A., Grothaus M., Hoh W., Kassmann M., Stannat W., Trutnau G. (eds) Stochastic Partial Differential Equations and Related Fields. SPDERF 2016. Springer Proceedings in Mathematics & Statistics, vol 229. Springer, Cham.

Corrigenda / Addenda

Working papers

    1. J. M. Tölle (with P. Beissner). A compact topology for σ-algebra convergence. Working paper, (2018), 23 pp., arXiv:1802.05920.
    2. J. M. Tölle. Convergence of solutions to the p-Laplace evolution equation as p goes to 1. Preprint,, 2011, 11 pp.