Time-like graphical models

Author(s)

• Tadić, Tvrtko

Bibliographic Information

Time-like graphical models

Tvrtko Tadić

（Memoirs of the American Mathematical Society, no. 1262）

American Mathematical Society, c2019

Note

"September 2019, volume 261, number 1262 (sixth of 7 numbers)"

Includes bibliographical reference (p. 167-168) and index

Description and Table of Contents

Description

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 extends the notion of time-like graphs and finds properties of processes indexed by them. In particular, the author solves the conjecture of uniqueness of the distribution for the process indexed by graphs with infinite number of vertices. The author provides a new result showing the stochastic heat equation as a limit of the sequence of natural Brownian motions on time-like graphs. In addition, the author's treatment of time-like graphical models reveals connections to Markov random fields, martingales indexed by directed sets and branching Markov processes.

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.

by "Nielsen BookData"

Details

• NCID: BB29356045
• ISBN:
  • 9781470436858
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Providence, R.I.
• Pages/Volumes: vii, 170 p.
• Size: 26 cm
• Parent Bibliography ID:
  • BA00035927