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Wresch, Lukas: Path by path uniqueness for stochastic differential equations in infinite dimensions. 2017
Inhalt
Introduction
The Story in a Nutshell
Our Contribution
Outline of the Proof
Structure of the Thesis
Acknowledgment
I Preliminaries
Girsanov Transformation
Framework & Main result
Reduction via Girsanov Transformation
Gronwall Inequalities
Linear Gronwall Inequalities
Log-Linear Gronwall Inequalities
Approximation Lattices
The effective Dimension of a Cuboid
The effective Dimension of the Set Q
II Hilbert space-valued Ornstein–Uhlenbeck Processes
Probabilistic Regularization by Noise
One-dimensional Ornstein–Uhlenbeck Processes
Hilbert space-valued Ornstein–Uhlenbeck Processes
A Concentration of Measure Result
Regularizing Noises
The Ornstein–Uhlenbeck Process is a Regularizing Noise
III Regularization by Noise
Pathwise Regularization by Noise
Estimate for x -3mun,k(x)
Estimate for (x,y) -3mun,k(x,y)
Continuity of bold0mu mumu n,kn,kDav07n,kn,kn,kn,k
A Uniform Bound for Regularizing Noises
The Approximation Theorem and Consequences thereof
Long-Time Regularization using Euler Approximations
Euler Approximations
Long-Time Regularization
Proof of the Main Result
Preparation
The Main Proof
Applications
Proof of the main result in abstract form
Proof of the main result
Finite-dimensional case
IV Bibliography