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" Stochastic partial differential equations and related fields : "
Andreas Eberle, Martin Grothaus, Walter Hoh, Moritz Kassmann, Wilhelm Stannat, Gerald Trutnau, editors.
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BL
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864758
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Conference "Stochastic Partial Differential Equations and Related Fields''(2016 :, Bielefeld, Germany)
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Stochastic partial differential equations and related fields : : in honor of Michael Röckner SPDERF, Bielefeld, Germany, October 10 -14, 2016 /\ Andreas Eberle, Martin Grothaus, Walter Hoh, Moritz Kassmann, Wilhelm Stannat, Gerald Trutnau, editors.
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| Publication Statement
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Cham, Switzerland :: Springer,, 2018.
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| Series Statement
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Springer proceedings in mathematics & statistics,; volume 229
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1 online resource (xx, 574 pages) :: illustrations
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3319749293
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: 9783319749297
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3319749285
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9783319749280
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Includes author index.
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| Contents
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Intro; Preface; Acknowledgements; Contents; Organization; List of Participants; Part I Longer Contributions; Stationary Fokker-Planck-Kolmogorov Equations; 1 Introduction; 2 The Case of a Non-differentiable Diffusion Matrix: Existence and Higher Integrability of Densities; 3 The Case of a Sobolev Differentiable Diffusion Matrix; 4 Harnack's Inequality and Lower and Upper Bounds; 5 Existence of Probability Solutions; 6 Uniqueness Problems; 7 The Infinite-Dimensional Case; References; Liouville Property of Harmonic Functions of Finite Energy for Dirichlet Forms; 1 Introduction
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2.2 Well-Posedness by Noise for Stochastic Inhomogeneous Scalar Conservation Laws2.3 Regularization by Noise for Stochastic Scalar Conservation Laws; 2.4 Open Interfaces and Porous Media Equations; References; An Introduction to Singular SPDEs; 1 Introduction; 2 Paraproducts; 3 Paracontrolled Analysis; 4 Ambiguities and Renormalisation; 5 Higher Order Expansions; 6 Weak Universality; 7 Anderson Hamiltonian; 8 Singular Martingale Problem; References; Fokker-Planck Equations in Hilbert Spaces; 1 Introduction and Setting of the Problem; 2 Preliminaries on the Ornstein-Uhlenbeck Semigroup
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3 Existence3.1 Basic Assumptions; 3.2 Tightness; 3.3 Other Assumptions; 4 Uniqueness; 4.1 The Rank Condition; 4.2 The Semigroup Associated to a Non Autonomous Problem; 4.3 The Case When C-1 is Bounded; 4.4 The Case When Tr C<infty; References; Part II Stochastic Partial Differential Equations and Regularity Structures; Stochastic and Deterministic Constrained Partial Differential Equations; 1 Introduction; 2 A Geometric Approach; 3 Constrained ``Heat'' Equation; 4 Local Existence and Invariance; 5 Applications; 5.1 Reaction Diffusion Equation; 5.2 Navier-Stokes Equations on a Torus mathbbT2
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6 Generalisation to Stochastic PDEsReferences; SPDEs with Volterra Noise; 1 Introduction; 2 SPDEs with Additive Volterra Noise; 3 SPDEs with Multiplicative Gaussian Volterra Noise; References; Hitting Probabilities for Systems of Stochastic PDEs: An Overview; 1 Introduction; 2 Benchmark Results for Gaussian Random Fields; 2.1 First Example: The Brownian Sheet; 2.2 Anisotropic Gaussian Random Fields; 2.3 Funaki's Random String; 3 Hitting Probabilities for Non-Gaussian Random Fields; 3.1 Systems of Nonlinear Wave Equations in Spatial Dimension 1; 3.2 Other Non-linear Systems of SPDEs
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This Festschrift contains six research surveys and thirty-three 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.--
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Stochastic partial differential equations, Congresses.
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Differential calculus equations.
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Mathematical modelling.
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MATHEMATICS-- Applied.
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MATHEMATICS-- Probability Statistics-- General.
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Probability statistics.
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Stochastic partial differential equations.
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Mathematical Applications in the Physical Sciences.
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| Dewey Classification
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519.2/2
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| LC Classification
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QA274.25
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| Added Entry
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Eberle, Andreas,1969-
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Grothaus, Martin, (Professor)
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Hoh, Walter
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Kassmann, Moritz
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Röckner, Michael,1956-
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Stannat, Wilhelm
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Trutnau, Gerald
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