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Project B1.1: New trends in stochastic partial differential equations: two types of transformations and a new notion of solution


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Summary:

This project consists of four parts: (I) Rescaling transformation for stochastic partial differential equations with linear multiplicative noise and their applications/consequences; (II) Low order regularity of Kolmogorov operators in infinite dimensional spaces and applications to stochastic partial differential equations; (III) Stochastic variational inequalities for stochastic partial differential equations; (IV) Mean field games and stochastic partial differential equations.


Recent Preprints:

24113 Theresa Lange, Marco Rehmeier, Andre Schenke PDF

Non-uniqueness of Leray–Hopf solutions for the 3D fractional Navier–Stokes equations perturbed by transport noise

Project: B1

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Non-uniqueness of Leray–Hopf solutions for the 3D fractional Navier–Stokes equations perturbed by transport noise


Authors: Theresa Lange, Marco Rehmeier, Andre Schenke Projects: B1
Submission Date: 20.03.2025 Submitter: Michael Röckner
Download: PDF Link: 24113

21036 Rongchan Zhu, Xiangchan Zhu, Martina Hofmanová PDF

Global-in-time probabilistically strong and Markov solutions to stochastic 3D Navier--Stokes equations: existence and non-uniqueness

Project: B1, B2, B7

Published: Ann. Probab. 51 (2023), 524–579

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Global-in-time probabilistically strong and Markov solutions to stochastic 3D Navier--Stokes equations: existence and non-uniqueness


Authors: Rongchan Zhu, Xiangchan Zhu, Martina Hofmanová Projects: B1, B2, B7
Submission Date: 04.05.2021 Submitter: Sebastian Herr
Download: PDF Link: 21036
Published: Ann. Probab. 51 (2023), 524–579

21029 Xiliang Fan, Michael Röckner, Shao-Qin Zhang PDF

A unified approach to gradient type formulas for BSDEs and some applications

Project: B1

To appear: Annales de l’Institut Henri Poincaré (2024)

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A unified approach to gradient type formulas for BSDEs and some applications


Authors: Xiliang Fan, Michael Röckner, Shao-Qin Zhang Projects: B1
Submission Date: 12.03.2021 Submitter: Benjamin Gess
Download: PDF Link: 21029
To appear: Annales de l’Institut Henri Poincaré (2024)

21028 Michael Röckner, Guohuan Zhao PDF

SDEs with critical time dependent drifts: Strong solutions

Project: B1

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SDEs with critical time dependent drifts: Strong solutions


Authors: Michael Röckner, Guohuan Zhao Projects: B1
Submission Date: 12.03.2021 Submitter: Benjamin Gess
Download: PDF Link: 21028

21012 Herbert Dawid, Martin Friesen, Oleksandr Kutoviy, Michael Röckner PDF

Mean-field analysis of industry dynamics under financial constraints

Project: A5, B1, C2

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Mean-field analysis of industry dynamics under financial constraints


Authors: Herbert Dawid, Martin Friesen, Oleksandr Kutoviy, Michael Röckner Projects: A5, B1, C2
Submission Date: 18.01.2021 Submitter: Frank Riedel
Download: PDF Link: 21012

20128 Xicheng Zhang PDF

Weak Solutions of McKean-Vlasov SDEs with Supercritical Drifts

Project: B1

Published: Communications in Mathematics and Statistics 12, no. 1 (2024), 1-14

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Weak Solutions of McKean-Vlasov SDEs with Supercritical Drifts


Authors: Xicheng Zhang Projects: B1
Submission Date: 30.12.2020 Submitter: Rongchan Zhu
Download: PDF Link: 20128
Published: Communications in Mathematics and Statistics 12, no. 1 (2024), 1-14

20127 Xicheng Zhang PDF

Maximum Principle for Non-Uniformly Parabolic Equations and Applications

Project: B1

Published: Ann. Scuola Norm. Sup. Pisa Cl. Sci. 25, no. 3 (2024), 1267–1308

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Maximum Principle for Non-Uniformly Parabolic Equations and Applications


Authors: Xicheng Zhang Projects: B1
Submission Date: 30.12.2020 Submitter: Rongchan Zhu
Download: PDF Link: 20127
Published: Ann. Scuola Norm. Sup. Pisa Cl. Sci. 25, no. 3 (2024), 1267–1308

20125 Xicheng Zhang, Rongchan Zhu, Xiangchan Zhu PDF

Singular HJB Equations with Applications to KPZ on the Real Line

Project: B1, B2

Published: Probab. Theory Relat. Fields 183, no. 3–4 (2022), 789–869

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Singular HJB Equations with Applications to KPZ on the Real Line


Authors: Xicheng Zhang, Rongchan Zhu, Xiangchan Zhu Projects: B1, B2
Submission Date: 30.12.2020 Submitter: Benjamin Gess
Download: PDF Link: 20125
Published: Probab. Theory Relat. Fields 183, no. 3–4 (2022), 789–869

20109 Michael Röckner, Guohuan Zhao PDF

SDEs with critical time dependent drifts: weak solutions

Project: A2, B1

Published: Bernoulli Journal 29, no. (1) (2023), 757 - 784

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SDEs with critical time dependent drifts: weak solutions


Authors: Michael Röckner, Guohuan Zhao Projects: A2, B1
Submission Date: 08.12.2020 Submitter: Martina Hofmanová
Download: PDF Link: 20109
Published: Bernoulli Journal 29, no. (1) (2023), 757 - 784

20107 Christian Vieth, L’ubomír Baňas, Benjamin Gess PDF

Numerical approximation of singular-degenerate parabolic stochastic PDEs

Project: B1, B3, B8

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Numerical approximation of singular-degenerate parabolic stochastic PDEs


Authors: Christian Vieth, L’ubomír Baňas, Benjamin Gess Projects: B1, B3, B8
Submission Date: 19.11.2020 Submitter: Sebastian Herr
Download: PDF Link: 20107


All Publications of this Project


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