Stochastic Partial Differential Equations and Related Fields

Table of Contents

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   Book Overview
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   Chapter 1 Stationary Fokker–Planck–Kolmogorov Equations
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   Chapter 2 Liouville Property of Harmonic Functions of Finite Energy for Dirichlet Forms
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   Chapter 3 Regularization and Well-Posedness by Noise for Ordinary and Partial Differential Equations
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   Chapter 4 An Introduction to Singular SPDEs
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   Chapter 5 Fokker–Planck Equations in Hilbert Spaces
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   Chapter 6 Stochastic and Deterministic Constrained Partial Differential Equations
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   Chapter 7 SPDEs with Volterra Noise
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   Chapter 8 Hitting Probabilities for Systems of Stochastic PDEs: An Overview
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    Chapter 9 Curvature Motion Perturbed by a Direction-Dependent Colored Noise
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    Chapter 10 Poisson Stochastic Process and Basic Schauder and Sobolev Estimates in the Theory of Parabolic Equations (Short Version)
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    Chapter 11 Dynamics of SPDEs Driven by a Small Fractional Brownian Motion with Hurst Parameter Larger than 1/2
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    Chapter 12 On the well-posedness of SPDEs with singular drift in divergence form
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    Chapter 13 Lower Bounds for Weak Approximation Errors for Spatial Spectral Galerkin Approximations of Stochastic Wave Equations
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    Chapter 14 Estimates for Nonlinear Stochastic Partial Differential Equations with Gradient Noise via Dirichlet Forms
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    Chapter 15 Random Data Cauchy Problem for Some Dispersive Equations
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    Chapter 16 SPDEs and Renormalisation
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    Chapter 17 Recent Progress on Stochastic Nonlinear Schrödinger Equations
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    Chapter 18 Generalized Solutions to Nonlinear Fokker–Planck Equations with Linear Drift
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    Chapter 19 Examples of renormalized SDEs
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    Chapter 20 Generalised Weitzenböck Formulae for Differential Operators in Hörmander Form
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    Chapter 21 On the Rough Gronwall Lemma and Its Applications
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    Chapter 22 Doubly Damped Stochastic Parallel Translations and Hessian Formulas
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    Chapter 23 Synchronization, Lyapunov Exponents and Stable Manifolds for Random Dynamical Systems
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    Chapter 24 Nonlinear Fokker–Planck–Kolmogorov Equations for Measures
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    Chapter 25 Coupling by Change of Measure, Harnack Inequality and Hypercontractivity
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    Chapter 26 Multidimensional Singular Stochastic Differential Equations
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    Chapter 27 Invariant, Super and Quasi-martingale Functions of a Markov Process
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    Chapter 28 Mean Value Inequalities for Jump Processes
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    Chapter 29 Positivity Preserving Semigroups and Positivity Preserving Coercive Forms
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    Chapter 30 Some Thoughts and Investigations on Densities of One-Parameter Operator Semi-groups
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    Chapter 31 Strong Uniqueness of Dirichlet Operators Related to Stochastic Quantization Under Exponential Interactions in One-Dimensional Infinite Volume
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    Chapter 32 A Probabilistic Proof of the Breakdown of Besov Regularity in L -Shaped Domains
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    Chapter 33 Symmetric Markov Processes with Tightness Property
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    Chapter 34 From non-symmetric particle systems to non-linear PDEs on fractals
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    Chapter 35 Probabilistic Approach to the Stochastic Burgers Equation
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    Chapter 36 Equilibrium States, Phase Transitions and Dynamics in Quantum Anharmonic Crystals
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    Chapter 37 On Continuous Coding
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    Chapter 38 Infinite-Dimensional Stochastic Differential Equations with Symmetry
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    Chapter 39 Recent Progress on the Dirichlet Forms Associated with Stochastic Quantization Problems