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Time-Like Graphical Models
 
Tvrtko Tadić :  University of Washington, Seattle, Washington, USA and University of Zagreb, Zagreb, Croatia
Time-Like Graphical Models
Time-Like Graphical Models
Softcover ISBN:  978-1-4704-3685-8
Product Code:  MEMO/261/1262
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
eBook ISBN:  978-1-4704-5416-6
Product Code:  MEMO/261/1262.E
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
Softcover ISBN:  978-1-4704-3685-8
eBook: ISBN:  978-1-4704-5416-6
Product Code:  MEMO/261/1262.B
List Price: $162.00$121.50
MAA Member Price: $145.80$109.35
AMS Member Price: $97.20$72.90
Add to cart
Time-Like Graphical Models
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Time-Like Graphical Models
Time-Like Graphical Models
Tvrtko Tadić :  University of Washington, Seattle, Washington, USA and University of Zagreb, Zagreb, Croatia
Softcover ISBN:  978-1-4704-3685-8
Product Code:  MEMO/261/1262
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
eBook ISBN:  978-1-4704-5416-6
Product Code:  MEMO/261/1262.E
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
Softcover ISBN:  978-1-4704-3685-8
eBook ISBN:  978-1-4704-5416-6
Product Code:  MEMO/261/1262.B
List Price: $162.00$121.50
MAA Member Price: $145.80$109.35
AMS Member Price: $97.20$72.90
Add to cart
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 261; 2019; 170 pp
    MSC: Primary 60; Secondary 05;

    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
     
     
    • Chapters
    • Introduction
    • 1. Construction and properties
    • 1. Geometry of time-like graphs
    • 2. Processes indexed by time-like graphs
    • 3. Markov properties of processes indexed by TLG’s
    • 4. Filtrations, martingales and stopping times
    • 2. Natural Brownian motion and the stochastic heat equation
    • 5. Maximums of Gaussian processes
    • 6. Random walk and stochastic heat equation reviewed
    • 7. Limit of the natural Brownian motion on a rhombus grid
    • 3. Processes on general and random time-like graphs
    • 8. Non-simple TLG’s
    • 9. Processes on non-simple TLG’s
    • 10. Galton-Watson time-like trees and the Branching Markov processes
    • Open questions and appendix
    • 11. Open questions
    • A. Independence and processes
    • Acknowledgments
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Memoirs of the American Mathematical Society
Volume: 261; 2019; 170 pp
MSC: Primary 60; Secondary 05;

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.
  • Chapters
  • Introduction
  • 1. Construction and properties
  • 1. Geometry of time-like graphs
  • 2. Processes indexed by time-like graphs
  • 3. Markov properties of processes indexed by TLG’s
  • 4. Filtrations, martingales and stopping times
  • 2. Natural Brownian motion and the stochastic heat equation
  • 5. Maximums of Gaussian processes
  • 6. Random walk and stochastic heat equation reviewed
  • 7. Limit of the natural Brownian motion on a rhombus grid
  • 3. Processes on general and random time-like graphs
  • 8. Non-simple TLG’s
  • 9. Processes on non-simple TLG’s
  • 10. Galton-Watson time-like trees and the Branching Markov processes
  • Open questions and appendix
  • 11. Open questions
  • A. Independence and processes
  • Acknowledgments
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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