Research

Home Research

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

David Hilbert

Webpage last updated February 23, 2024

  • 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 B. Avelin, T. Kuusi, P. Nummi, E. Saksman and L. Viitasaari). 1D stochastic pressure equation with log-correlated Gaussian coefficients. Preprint, submitted (2024), 37 pp., arXiv:2402.09127.

Accepted for journal publication

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. https://doi.org/10.1007/978-3-319-74929-7_14.

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, http://arxiv.org/abs/1103.0229v2, 2011, 11 pp.

Theses