Description
Book SynopsisThe author studies continuous processes indexed by a special family of graphs. Processes indexed by vertices of graphs are known as probabilistic graphical models. In 2011, Burdzy and Pal proposed a continuous version of graphical models indexed by graphs with an embedded time structure - so-called time-like graphs.
Table of Contents
- Introduction
- Part 1. Construction and properties: Geometry of time-like graphs
- Processes indexed by time-like graphs
- Markov properties of processes indexed by TLG's
- Filtrations, martingales and stopping times
- Part 2. Natural Brownian motion and the stochastic heat equation: Maximums of Gaussian processes
- Random walk and stochastic heat equation reviewed
- Limit of the natural Brownian motion on a rhombus grid
- Part 3. Processes on general and random time-like graphs: Non-simple TLG's
- Processes on non-simple TLG's
- Galton-Watson time-like trees and the Branching Markov processes
- Open questions and appendix: Open questions
- Appendix A. Independence and processes
- Acknowledgments
- Bibliography
- Index.
