Jonas Tölle
University Lecturer
Docent in Mathematics
Dr. math. habil.
Preferred way of contact:
jonasmtoelle [usual symbol] gmail.com

Jonas Tölle is a mathematician with research topics ranging from nonlinear functional and variational analysis, stochastic analysis and theory and applications of stochastic partial differential equations. Currently (in 2023), he has a position as a University Lecturer (yliopistonlehtori) for Mathematics and Statistics at the Department of Mathematics and Systems Analysis at the Aalto University, Finland. He is also a Docent (dosentti) in mathematics at the University of Helsinki. He has also worked as a part-time photographer/photojournalist.
Memberships
European Mathematical Society (EMS)
Finnish Mathematical Society (SMY)
German Mathematical Society (DMV)
Suomen tiedetoimittajain liitto ry (Finnish association of science editors and journalists)
“He who seeks for methods without having a definite problem in mind seeks for the most part in vain.”
David Hilbert
Webpage last updated November 4, 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
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- J. M. Tölle (with I. Ciotir and D. Goreac). Improved regularity for the stochastic fast diffusion equation. Preprint, submitted (2023), 7 pp., arXiv:2310.01328.
Accepted for journal publication
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- J. M. Tölle (with E. Hausenblas). The stochastic Klausmeier system and a stochastic Schauder-Tychonoff type theorem. To appear in Potential Analysis (2023+), 62 pp., https://doi.org/10.1007/s11118-023-10107-3, author accepted manuscript available at arXiv:1912.00996.
Journal Publications
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- 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.
- 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.
- J. M. Tölle (with F. Seib and W. Stannat). Stability and moment estimates for the stochastic singular Φ-Laplace equation. J. Differential Equations 377 (2023), 663–693, https://doi.org/10.1016/j.jde.2023.09.019, author accepted manuscript available at arXiv:2103.03194.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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
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- 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
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- 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
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- J. M. Tölle (with P. Beissner). A compact topology for σ-algebra convergence. Working paper, (2018), 23 pp., arXiv:1802.05920.
- 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
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- 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.
- 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.
- 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)
- 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