The 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.
The 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.
Tvrtko Tadic, University of Washington, Seattle, Washington, and University of Zagreb, Croatia.
Inhaltsangabe
1. Introduction 2. Part 1. Construction and properties: Geometry of time-like graphs 3. Processes indexed by time-like graphs 4. Markov properties of processes indexed by TLG's 5. Filtrations, martingales and stopping times 6. Part 2. Natural Brownian motion and the stochastic heat equation: Maximums of Gaussian processes 7. Random walk and stochastic heat equation reviewed 8. Limit of the natural Brownian motion on a rhombus grid 9. Part 3. Processes on general and random time-like graphs: Non-simple TLG's 10. Processes on non-simple TLG's 11. Galton-Watson time-like trees and the Branching Markov processes 12. Open questions and appendix: Open questions 13. Appendix A. Independence and processes 14. Acknowledgments 15. Bibliography 16. Index.
1. Introduction 2. Part 1. Construction and properties: Geometry of time-like graphs 3. Processes indexed by time-like graphs 4. Markov properties of processes indexed by TLG's 5. Filtrations, martingales and stopping times 6. Part 2. Natural Brownian motion and the stochastic heat equation: Maximums of Gaussian processes 7. Random walk and stochastic heat equation reviewed 8. Limit of the natural Brownian motion on a rhombus grid 9. Part 3. Processes on general and random time-like graphs: Non-simple TLG's 10. Processes on non-simple TLG's 11. Galton-Watson time-like trees and the Branching Markov processes 12. Open questions and appendix: Open questions 13. Appendix A. Independence and processes 14. Acknowledgments 15. Bibliography 16. Index.
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