Altemeier, Daniel: Concentration Inequalities for Nonautonomous Stochastic Delay Differential Equations. 2017
Inhalt
- Introduction
- The Fernique Inequality: A Concentration Inequality for Gaussian Processes
- On Stochastic Functional Differential Equations
- Definitions and Conventions
- General Existence and Uniqueness of Solutions
- Representations for Linear RFDEs with Additive Noise
- Concentration of Sample Paths in Autonomous Stable Environment
- Stochastic Delay Differential Equations
- Convergence in Critical Regime
- Consequences of Convergence
- Concentration Results for SDDEs
- Small-Ball Probabilities
- From Uniform Stability to Instability
- Setting and the Replacement System
- Uniform Stability
- Transition - Stability Comes to an End
- Shallow Curvature
- The End of Stability
- During a Small Time at Instability
- Uniformly Symmetric Environment
- On the Choice of Delay Influence
- Departure From Instability
- Auxiliaries
- A Concentration Result for linear SDEs
- Estimates for Q-integrals
- Brownian First-Exit Distribution - Lower Tail Estimates
- SDDEs - Case Studies
- REFERENCES