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Project A2: Singular integral operators and stochastic processes


Principal Investigator(s)
Moritz Kaßmann
Visitor(s)
Currently no visitors.

Summary:

We develop a mathematical theory for nonlocal and discrete differential operators, which are related to Markov processes on subsets of the Euclidean space or graphs. We focus on results which are crucial for an understanding of the underlying dynamics independent of regularity assumptions on the state space or inhomogeneities of the medium. In this project, we study the following two interrelated parts, which go beyond current research and provide several new mathematical challenges: (I) Nonlocal operators with logarithmic order of differentiability and (II) Nonlocal operators and Markov processes on graphs.


Recent Preprints:

19101 Guohuan Zhao PDF

Stochastic Lagrangian flows for SDES with rough coefficients

Project: A2

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Stochastic Lagrangian flows for SDES with rough coefficients


Authors: Guohuan Zhao Projects: A2
Submission Date: 13.11.2019 Submitter: Sebastian Herr
Download: PDF Link: 19101

19081 Guohuan Zhao PDF

On the Malliavin differantiability and flow property of solutions to Lévy noise driven SDE's with irregular coefficients

Project: A2

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On the Malliavin differantiability and flow property of solutions to Lévy noise driven SDE's with irregular coefficients


Authors: Guohuan Zhao Projects: A2
Submission Date: 02.10.2019 Submitter: Michael Röckner
Download: PDF Link: 19081

19076 Xicheng Zhang, Guohuan Zhao PDF

Stochastic Langrangian path for Leray solutions of 3D Navier-Stokes equations

Project: A2, B1

To appear: Communications in Mathematical Physics (2020)

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Stochastic Langrangian path for Leray solutions of 3D Navier-Stokes equations


Authors: Xicheng Zhang, Guohuan Zhao Projects: A2, B1
Submission Date: 01.10.2019 Submitter: Michael Röckner
Download: PDF Link: 19076
To appear: Communications in Mathematical Physics (2020)

19075 Pengcheng Xia, Longjie Xie, Xicheng Zhang, Guohuan Zhao PDF

$L^{q}(L^p)$-Theory of stochastic differential equations

Project: A2, B1

Published: Stochastic Processes and their Applications 130, no. 8 (2020), 5188-5211

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$L^{q}(L^p)$-Theory of stochastic differential equations


Authors: Pengcheng Xia, Longjie Xie, Xicheng Zhang, Guohuan Zhao Projects: A2, B1
Submission Date: 01.10.2019 Submitter: Michael Röckner
Download: PDF Link: 19075
Published: Stochastic Processes and their Applications 130, no. 8 (2020), 5188-5211

18078 Grzegorz Karch, Moritz Kaßmann, Milosz Krupski PDF

A framework for non-local, non-linear initial value problems

Project: A2

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A framework for non-local, non-linear initial value problems


Authors: Grzegorz Karch, Moritz Kaßmann, Milosz Krupski Projects: A2
Submission Date: 23.12.2018 Submitter: Alexander Grigor'yan
Download: PDF Link: 18078

18077 Jamil Chaker, Moritz Kaßmann PDF

Nonlocal operators with singular anisotropic kernels

Project: A2

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Nonlocal operators with singular anisotropic kernels


Authors: Jamil Chaker, Moritz Kaßmann Projects: A2
Submission Date: 23.12.2018 Submitter: Alexander Grigor'yan
Download: PDF Link: 18077

18076 Moritz Kaßmann, Vanja Wagner PDF

Nonlocal quadratic forms with visibility constraint

Project: A2

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Nonlocal quadratic forms with visibility constraint


Authors: Moritz Kaßmann, Vanja Wagner Projects: A2
Submission Date: 23.12.2018 Submitter: Alexander Grigor'yan
Download: PDF Link: 18076

18075 Moritz Kaßmann, Andrey Piatnitski, Elena Zhizhina PDF

Homogenization of Lévy-type operators with oscillating coefficients

Project: A2

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Homogenization of Lévy-type operators with oscillating coefficients


Authors: Moritz Kaßmann, Andrey Piatnitski, Elena Zhizhina Projects: A2
Submission Date: 23.12.2018 Submitter: Alexander Grigor'yan
Download: PDF Link: 18075

18070 Xicheng Zhang, Guohuan Zhao PDF

Dirichlet problem for supercritical non-local operators

Project: A2, B1

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Dirichlet problem for supercritical non-local operators


Authors: Xicheng Zhang, Guohuan Zhao Projects: A2, B1
Submission Date: 17.12.2018 Submitter: Michael Röckner
Download: PDF Link: 18070

18069 Xicheng Zhang, Guohuan Zhao PDF

Singular Brownian Diffusion Processes

Project: A2, B1

Published: Communications in Mathematics and Statistics 6 (2018), 533–581

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Singular Brownian Diffusion Processes


Authors: Xicheng Zhang, Guohuan Zhao Projects: A2, B1
Submission Date: 17.12.2018 Submitter: Michael Röckner
Download: PDF Link: 18069
Published: Communications in Mathematics and Statistics 6 (2018), 533–581



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