Linear and Non-linear Deformations of Stochastic Processes

The aim of this section is to provide some background material and inspire, together with in short summarize, the content of the first 2 papers of this dissertation. At the very hart of Hilbert space theory and its apps lies the concept of an orthonormal sequence, i.e. a sequence of pairwise orthogonal elements of norm one from the underlying space. Let’s begin by talking about 2 diverse directions,followed to great length in the current literature, along which the perception of an orthonormal series continues to be generalized.

Contents: Linear and Non-linear Deformations of Stochastic Processes

Introduction
1. Riesz bases, frames and weakly stationary processes
1.1. Riesz bases and frames

1.2. Weakly stationary stochastic processes
1.3. Paper 1: Riesz bases andUBLS sequences
1.4. Paper 2: Frames, covariance functions and regular sequences
2. Multifunctions andmultiprocesses. Gauges andmultigauges
2.1. Analyticmultifunctions
2.2. Holomorphic, subharmonic and subholomorphic processes
2.3. Gauges andmultigauges of functions andmultifunctions
2.4. Paper 3: Gauges and multigauges of processes and multiprocesses
References
Approximate stationarity and Riesz bases
1. Introduction
2. Covariance functions, UBLS and bistationary sequences
3. Finite dimensional stationary and UBLS sequences
4. The algebra A of pseudomeasures and convolution in 2(Z)
5. Regular UBLS sequences and weakly stationary Riesz bases
6. Perturbations of weakly stationary sequences. Addition of noise
References
Operators preserving regularity and regular frames
1. Introduction
2. Notations and setup
3. Approximate stationarity and frames
4. Regular frames and regularity preserving operators
References
Gauges and multigauges of stochastic processes
1. Introduction
2. Set-up
3. Gauges of stochastic processes…