Research

Submitted for peer review

• 1. J. M. Tölle (with M. Hinz and L. Viitasaari). On fractal minimizers and potentials of occupation measures. Preprint, submitted (2025), 28 pp., arXiv:2512.14248.
  2. J. M. Tölle (with A.-M. Otsetova). Ergodicity for stochastic neural field equations. Preprint, submitted (2025), 30 pp., arXiv:2505.14012.
  3. J. M. Tölle (with G. Barrera). Ergodicity and mixing for locally monotone stochastic evolution equations. Preprint, submitted (2024), 44 pp., arXiv:2412.01381.

Journal Publications

• 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. Stochastic Processes and their Applications 192 (2026), no. 104808, 1–23, https://doi.org/10.1016/j.spa.2025.104808, author accepted manuscript available at arXiv:2402.09127.
  2. J. M. Tölle (with B. Avelin, T. Kuusi, P. Nummi, E. Saksman and L. Viitasaari). Renormalized stochastic pressure equation with log-correlated Gaussian coefficients. Journal of Differential Equations 439 (2025), no. 113416, 1–38, https://doi.org/10.1016/j.jde.2025.113416, author accepted manuscript available at arXiv:2405.17195.
  3. J. M. Tölle (with M. Hinz and L. Viitasaari). Variability and the existence of rough integrals with irregular coefficients. Electronic Communications in Probability 30 (2025), no. 7, 1–12, https://doi.org/10.1214/25-ECP656, author accepted manuscript available at arXiv:2407.06907.
  4. J. M. Tölle (with E. Hausenblas). The stochastic Klausmeier system and a stochastic Schauder-Tychonoff type theorem. Potential Analysis 61 (2024), no. 2, 185–246, https://doi.org/10.1007/s11118-023-10107-3, author accepted manuscript available at arXiv:1912.00996.
  5. J. M. Tölle (with I. Ciotir and D. Goreac). Improved regularity for the stochastic fast diffusion equation. Electronic Communications in Probability 29 (2024), no. 5, 1–7, https://doi.org/10.1214/24-ECP575, author accepted manuscript available at arXiv:2310.01328.
  6. J. M. Tölle (with M. Hinz and L. Viitasaari). Variability of paths and differential equations with BV-coefficients. Annales de l’Institut Henri Poincaré (B) – Probabilités et Statistiques 59 (2023), no. 4, 2036–2082, https://doi.org/10.1214/22-AIHP1308, author accepted manuscript available at arXiv:2003.11698.
  7. J. M. Tölle (with D. Blömker). Singular limits for stochastic equations. Stochastics and Dynamics, 23 (2023), no. 05, 2350040, 1–25, https://doi.org/10.1142/S0219493723500405, author accepted manuscript available at arXiv:2204.09545.
  8. J. M. Tölle (with F. Seib and W. Stannat). Stability and moment estimates for the stochastic singular Φ-Laplace equation. Journal of Differential Equations 377 (2023), 663–693, https://doi.org/10.1016/j.jde.2023.09.019, author accepted manuscript available at arXiv:2103.03194.
  9. J. M. Tölle (with M. Hinz and L. Viitasaari). Sobolev regularity of occupation measures and paths, variability and compositions. Electronic Journal of Probability 27 (2022), no. 73, 1–29, https://doi.org/10.1214/22-EJP797, preprint available at arXiv:2105.06249.
  10. J. M. Tölle. Stochastic evolution equations with singular drift and gradient noise via curvature and commutation conditions. Stochastic Processes and their Applications, 130 (2020), no. 5, 3220–3248, https://doi.org/10.1016/j.spa.2019.09.011, preprint available at arXiv:1803.07005.
  11. J. M. Tölle (with C. Kuehn). A gradient flow formulation for the stochastic Amari neural field model. Journal of Mathematical Biology 79 (2019), no. 4, 1227–1252, https://doi.org/10.1007/s00285-019-01393-w, preprint available at arXiv:1807.02575.
  12. J. M. Tölle (with B. Gess). Ergodicity and local limits for stochastic local and nonlocal p-Laplace equations. SIAM Journal on Mathematical Analysis 48 (2016), no. 6, 4094–4125, http://dx.doi.org/10.1137/15M1049774, preprint available at arXiv:1507.04545.
  13. J. M. Tölle (with I. Ciotir). Nonlinear stochastic partial differential equations with singular diffusivity and gradient Stratonovich noise. Journal of Functional Analysis 271 (2016), no. 7, 1764–1792, http://dx.doi.org/10.1016/j.jfa.2016.05.013, preprint available at arXiv:1507.02576.
  14. J. M. Tölle (with B. Gess). Stability of solutions to stochastic partial differential equations. Journal of Differential Equations 260 (2016), no. 6, 4973–5025, http://dx.doi.org/10.1016/j.jde.2015.11.039, preprint available at arXiv:1506.01230.
  15. J. M. Tölle (with B. Gess). Multi-valued, singular stochastic evolution inclusions. Journal de Mathématiques Pures et Appliquées 101 (2014), no. 6, 789–827, http://dx.doi.org/10.1016/j.matpur.2013.10.004, preprint available at arXiv:1112.5672.
  16. J. M. Tölle (with A. Es-Sarhir, M. Scheutzow and O. van Gaans). Invariant measures for monotone SPDEs with multiplicative noise term. Applied Mathematics and Optimization 68 (2013), no. 2, 275–287, http://dx.doi.org/10.1007/s00245-013-9206-4, preprint available at arXiv:0910.0960.
  17. J. M. Tölle. Uniqueness of weighted Sobolev spaces with weakly differentiable weights. Journal of Functional Analysis 263 (2012), no. 10, 3195–3223, http://dx.doi.org/10.1016/j.jfa.2012.08.002, preprint available at arXiv:1110.2888.
  18. J. M. Tölle (with I. Ciotir). Convergence of invariant measures for singular stochastic diffusion equations. Stochastic Processes and their Applications 122 (2012), no. 4, 1998–2017, http://dx.doi.org/10.1016/j.spa.2011.11.011, preprint available at arXiv:1201.2839.
  19. J. M. Tölle (with M.-K. von Renesse). On an EVI curve characterization of Hilbert spaces. Journal of Mathematical Analysis and Applications 385 (2012), 589–598, http://dx.doi.org/10.1016/j.jmaa.2011.06.080.
  20. J. M. Tölle (with W. Liu). Existence and uniqueness of invariant measures for stochastic evolution equations with weakly dissipative drifts. Electronic Communications in Probability 16 (2011), 447–457, https://doi.org/10.1214/ECP.v16-1643, preprint available at arXiv:1109.2437.

Accepted for publication in peer reviewed proceedings

• 1. J. M. Tölle (with I. Ciotir and D. Goreac). Stochastic evolution equations with nonlinear diffusivity, recent progress and critical cases. To appear in Stochastic analysis for irregular stochastic and deterministic models, Winter School CIRM Marseille, January 8-12th 2024, Springer Nature, 2026, 14 pp., author accepted manuscript available at arXiv:2510.20471.

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, 2018, pp. 249–262. https://doi.org/10.1007/978-3-319-74929-7_14.

Corrigenda / Addenda

• 1. J. M. Tölle (with I. Ciotir). Corrigendum to “Convergence of invariant measures for singular stochastic diffusion equations” [Stochastic Process. Appl. 122 (2012) 1998–2017.] Stochastic Processes and their Applications 123 (2013), no. 3, 1178–1181, http://dx.doi.org/10.1016/j.spa.2012.10.009, preprint available at arXiv:1211.4404.

Working papers

• 1. 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

• 1. J. M. Tölle. Stochastic partial differential equations with singular drift. Habilitation thesis, Universität Augsburg, 2019, 232 pp, https://opus.bibliothek.uni-augsburg.de/opus4/84117.
  2. J. M. Tölle. Variational convergence of nonlinear partial differential operators on varying Banach spaces. Dissertation, Universität Bielefeld, published online on BieSOn, Universitätsbibliothek Bielefeld, urn:nbn:de:hbz:361-16758, 2010, 250 pp, pdf.
  3. J. M. Tölle. Convergence of non-symmetric forms with changing reference measures. Diploma thesis, Universität Bielefeld, BiBoS-Preprint E06-09-234, http://www.math.uni-bielefeld.de/~bibos/preprints/E06-09-234.pdf, 2006, 81 pp.

(in chronological order – most recent first)

• Anna-Mariya Otsetova
• Gerardo Barrera
• Benny Avelin
• Tuomo Kuusi
• Patrik Nummi
• Eero Saksman
• Dan Goreac
• Dirk Blömker
• Florian Seib
• Wilhelm Stannat
• Michael Hinz
• Lauri Viitasaari
• Erika Hausenblas
• Christian Kuehn
• Patrick Beissner
• Abdelhadi Es-Sarhir
• Michael Scheutzow
• Onno van Gaans
• Benjamin Gess
• Max-K. von Renesse
• Wei Liu
• Ioana Ciotir

Erdős number: 3
P. Erdős — C. J. Colbourn — M. Scheutzow — J. M. Tölle

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