Research

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

• 1. 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.
  2. 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.
  3. 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.
  4. J. M. Tölle (with B. Gess). Ergodicity and local limits for stochastic local and nonlocal p-Laplace equations. SIAM J. Math. Anal. 48 (2016), no. 6, 4094–4125, http://dx.doi.org/10.1137/15M1049774, preprint available at arXiv:1507.04545.
  5. J. M. Tölle (with I. Ciotir). Nonlinear stochastic partial differential equations with singular diffusivity and gradient Stratonovich noise. J. Funct. Anal. 271 (2016), no. 7, 1764–1792, http://dx.doi.org/10.1016/j.jfa.2016.05.013, preprint available at arXiv:1507.02576.
  6. J. M. Tölle (with B. Gess). Stability of solutions to stochastic partial differential equations. J. 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.
  7. J. M. Tölle (with B. Gess). Multi-valued, singular stochastic evolution inclusions. J. Math. Pures Appl. 101 (2014), no. 6, 789–827, http://dx.doi.org/10.1016/j.matpur.2013.10.004, preprint available at arXiv:1112.5672.
  8. J. M. Tölle (with A. Es-Sarhir, M. Scheutzow and O. van Gaans). Invariant measures for monotone SPDEs with multiplicative noise term. Appl. Math. Optim. 68 (2013), no. 2, 275–287, http://dx.doi.org/10.1007/s00245-013-9206-4, preprint available at arXiv:0910.0960.
  9. J. M. Tölle. Uniqueness of weighted Sobolev spaces with weakly differentiable weights. J. Funct. Anal. 263 (2012), no. 10, 3195–3223, http://dx.doi.org/10.1016/j.jfa.2012.08.002, preprint available at arXiv:1110.2888.
  10. J. M. Tölle (with I. Ciotir). Convergence of invariant measures for singular stochastic diffusion equations. Stochastic Process. Appl. 122 (2012), no. 4, 1998–2017, http://dx.doi.org/10.1016/j.spa.2011.11.011, preprint available at arXiv:1201.2839.
  11. J. M. Tölle (with M.-K. von Renesse). On an EVI curve characterization of Hilbert spaces. J. Math. Anal. Appl. 385 (2012), 589–598, http://dx.doi.org/10.1016/j.jmaa.2011.06.080.
  12. J. M. Tölle (with W. Liu). Existence and uniqueness of invariant measures for stochastic evolution equations with weakly dissipative drifts. Electr. Comm. Probab. 16 (2011), 447–457, https://doi.org/10.1214/ECP.v16-1643, preprint available at arXiv:1109.2437.

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

• 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 Process. Appl. 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 (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

• 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)

• 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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