Goodair D. Stochastic Calculus in Infinite Dimensions and SPDEs 2024
Download this torrent!
Goodair D. Stochastic Calculus in Infinite Dimensions and SPDEs 2024
To start this P2P download, you have to install a BitTorrent client like qBittorrent
Category: Other
Total size: 4.86 MB
Added: 2025-03-10 23:39:01
Share ratio:
5 seeders,
4 leechers
Info Hash: 5FA26CD9DA48378E1A7D07E3B8CA342F5A86C31D
Last updated: 9.6 hours ago
Description:
Textbook in PDF format
Introducing a groundbreaking framework for stochastic partial differential equations (SPDEs), this work presents three significant advancements over the traditional variational approach.
Firstly, Stratonovich SPDEs are explicitly addressed. Widely used in physics, Stratonovich SPDEs have typically been converted to Ito form for mathematical treatment. While this conversion is understood heuristically, a comprehensive treatment in infinite dimensions has been lacking, primarily due to insufficient rigorous results on martingale properties.
Secondly, the framework incorporates differential noise, assuming the noise operator is only bounded from a smaller Hilbert space into a larger one, rather than within the same space. This necessitates additional regularity in the Ito form to solve the original Stratonovich SPDE. This aspect has been largely overlooked, despite the increasing popularity of gradient-dependent Stratonovich noise in fluid dynamics and regularisation by noise studies.
Lastly, the framework departs from the explicit duality structure (Gelfand Triple), which is typically expected in the study of analytically strong solutions. This extension builds on the classical variational framework established by Röckner and Pardoux, advancing it in all three key aspects.
Explore this innovative approach that not only addresses existing challenges but also opens new avenues for research and application in SPDEs.
Preface
Acknowledgements
Introduction
Motivation and Description of the Brief
Notation
Stochastic Calculus in Infinite Dimensions
A Classical Construction for Hilbert Space Valued Processes
Martingale and Local Martingale Integrators
Cylindrical Brownian Motion
Martingale Theory in Hilbert Spaces
Integration with Respect to Cylindrical Brownian Motion
Stochastic Differential Equations in Infinite Dimensions
The Stratonovich Integral
Strong Solutions in the Abstract Framework
Uniqueness and Maximality
Stratonovich SPDEs in the Abstract Framework
Weak Solutions in the Abstract Framework
Time-Dependent Operators
Toolbox for Nonlinear SPDEs
Existence and Uniqueness in Finite Dimensions
Tightness Criteria
Cauchy Criteria
Enhanced Regularity and an Energy Equality
SPDEs with Constant Multiplicative Noise
Appendix A
Classical Results from the Real Valued Theory
Classical Tightness Criteria
Stochastic Grönwall Lemma
References
Index