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Stochastic Partial Differential Equations and Related Fields

In Honor of Michael Röckner SPDERF, Bielefeld, Germany, October 10 -14, 2016

  • Conference proceedings
  • © 2018

Overview

Editors:
  1. Andreas Eberle

    1. Institute for Applied Mathematics, University of Bonn, Bonn, Germany

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  2. Martin Grothaus

    1. Fachbereich Mathematik, Technische Universität Kaiserslautern, Kaiserslautern, Germany

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  3. Walter Hoh

    1. Faculty of Mathematics, Bielefeld University, Bielefeld, Germany

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  4. Moritz Kassmann

    1. Faculty of Mathematics, Bielefeld University, Bielefeld, Germany

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  5. Wilhelm Stannat

    1. Institut für Mathematik, Technische Universität Berlin, Berlin, Germany

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  6. Gerald Trutnau

    1. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul, Korea (Republic of)

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  • Introduces a well-described research field related to Stochastic Partial Differential Equations and Stochastic Analysis
  • Includes a large amount of research surveys
  • Presents the current state of the art and promising future developments

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 229)

Included in the following conference series:

Conference proceedings info: SPDERF 2016.

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Table of contents (39 papers)

  1. Front Matter

    Pages i-xx
    Download chapter PDF

  2. Longer Contributions

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. Stationary Fokker–Planck–Kolmogorov Equations

      • Vladimir I. Bogachev
      Pages 3-24

    3. Liouville Property of Harmonic Functions of Finite Energy for Dirichlet Forms

      • Masatoshi Fukushima
      Pages 25-42

    4. Regularization and Well-Posedness by Noise for Ordinary and Partial Differential Equations

      • Benjamin Gess
      Pages 43-67

    5. An Introduction to Singular SPDEs

      • Massimiliano Gubinelli, Nicolas Perkowski
      Pages 69-99

    6. Fokker–Planck Equations in Hilbert Spaces

      • Giuseppe Da Prato
      Pages 101-129

  3. Stochastic Partial Differential Equations and Regularity Structures

    1. Front Matter

      Pages 131-131
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    2. Stochastic and Deterministic Constrained Partial Differential Equations

      • Zdzisław Brzeźniak, Gaurav Dhariwal, Javed Hussain, Mauro Mariani
      Pages 133-146

    3. SPDEs with Volterra Noise

      • Petr Čoupek, Bohdan Maslowski, Jana Šnupárková
      Pages 147-158

    4. Hitting Probabilities for Systems of Stochastic PDEs: An Overview

      • Robert C. Dalang
      Pages 159-176

    5. Curvature Motion Perturbed by a Direction-Dependent Colored Noise

      • Clément Denis, Tadahisa Funaki, Satoshi Yokoyama
      Pages 177-200

    6. Poisson Stochastic Process and Basic Schauder and Sobolev Estimates in the Theory of Parabolic Equations (Short Version)

      • N. V. Krylov, E. Priola
      Pages 201-211

    7. Dynamics of SPDEs Driven by a Small Fractional Brownian Motion with Hurst Parameter Larger than 1/2

      • L. H. Duc, M. J. Garrido-Atienza, B. Schmalfuß
      Pages 213-224

    8. On the Well-Posedness of SPDEs with Singular Drift in Divergence Form

      • Carlo Marinelli, Luca Scarpa
      Pages 225-235

    9. Lower Bounds for Weak Approximation Errors for Spatial Spectral Galerkin Approximations of Stochastic Wave Equations

      • Ladislas Jacobe de Naurois, Arnulf Jentzen, Timo Welti
      Pages 237-248

    10. Estimates for Nonlinear Stochastic Partial Differential Equations with Gradient Noise via Dirichlet Forms

      • Jonas M. Tölle
      Pages 249-262

    11. Random Data Cauchy Problem for Some Dispersive Equations

      • Wei Yan, Jinqiao Duan
      Pages 263-269

    12. SPDEs and Renormalisation

      • Lorenzo Zambotti
      Pages 271-277

    13. Recent Progress on Stochastic Nonlinear Schrödinger Equations

      • Deng Zhang
      Pages 279-289
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Other volumes

  1. Stochastic Partial Differential Equations and Related Fields

Keywords

About this book

This Festschrift contains five research surveys and thirty-four shorter contributions by participants of the conference ''Stochastic Partial Differential Equations and Related Fields'' hosted by the Faculty of Mathematics at Bielefeld University, October 10–14, 2016. The conference, attended by more than 140 participants, including PostDocs and PhD students, was held both to honor Michael Röckner's contributions to the field on the occasion of his 60th birthday and to bring together leading scientists and young researchers to present the current state of the art and promising future developments.

Each article introduces a well-described field related to Stochastic Partial Differential Equations and Stochastic Analysis in general. In particular, the longer surveys focus on Dirichlet forms and Potential theory, the analysis of Kolmogorov operators, Fokker–Planck equations in Hilbert spaces, the theory of variational solutions to stochastic partial differential equations, singular stochastic partial differential equations and their applications in mathematical physics, as well as on the theory of regularity structures and paracontrolled distributions.

The numerous research surveys make the volume especially useful for graduate students and researchers who wish to start work in the above-mentioned areas, or who want to be informed about the current state of the art.




Editors and Affiliations

  • Institute for Applied Mathematics, University of Bonn, Bonn, Germany

    Andreas Eberle

  • Fachbereich Mathematik, Technische Universität Kaiserslautern, Kaiserslautern, Germany

    Martin Grothaus

  • Faculty of Mathematics, Bielefeld University, Bielefeld, Germany

    Walter Hoh, Moritz Kassmann

  • Institut für Mathematik, Technische Universität Berlin, Berlin, Germany

    Wilhelm Stannat

  • Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul, Korea (Republic of)

    Gerald Trutnau

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