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|a 1130765898
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|a 1470454165
|q (electronic book)
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|a (OCoLC)1130900404
|z (OCoLC)1130765898
|z (OCoLC)1266287113
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|a QA273.5
|b .T33 2019
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|a HCDD
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|a Tadić, Tvrtko,
|e author.
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|a Time-like graphical models /
|c Tvrtko Tadić.
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|a Providence, RI :
|b American Mathematical Society,
|c [2019]
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|c ©2019
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| 300 |
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|a 1 online resource (vii, 184 pages) :
|b illustrations
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| 336 |
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
|2 rdacarrier
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|a Memoirs of the American Mathematical Society ;
|v number 1262
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|a Cover -- Title page -- Introduction -- Construction and properties -- Natural Brownian motion and the stochastic heat equation -- Processes on general and random time-like graphs -- Open questions and appendix -- Part 1 . Construction and properties -- Chapter 1. Geometry of time-like graphs -- 1.1. Basic definitions -- 1.2. TLG* family -- 1.3. Consistent representation of a TLG*-tower, spines and (re)construction -- 1.4. Interval TLG*'s -- 1.5. Topology on TLG's -- 1.6. TLG* as a topological lattice -- 1.7. Cell collapse transformation and the stingy algorithm
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|a 1.8. TLG's with infinitely many vertices -- Chapter 2. Processes indexed by time-like graphs -- 2.1. Spine-Markovian property -- 2.2. Consistent distributions on paths -- 2.3. Construction from a consistent family -- 2.4. Processes on TLG's with infinite number of vertices -- Chapter 3. Markov properties of processes indexed by TLG's -- 3.1. Cell-Markov properties -- 3.2. Graph-Markovian and time-Markovian property -- 3.3. Processes on TLG's for Markov family \cM -- 3.4. Homogeneous Markov family \cM_{\cP} -- 3.5. Three simple examples -- Chapter 4. Filtrations, martingales and stopping times
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|a 4.1. Expanding the filtrations -- 4.2. Markov martingales -- 4.3. Optional sampling theorem for martingales indexed by directed sets -- 4.4. TLG -- valued stopping times -- 4.5. A simple coupling and branching process -- Part 2 . Natural Brownian motion and the stochastic heat equation -- Chapter 5. Maximums of Gaussian processes -- 5.1. Sequence of Brownian bridges -- 5.2. Sequence of normal variables -- 5.3. Some concentration and convergence results -- Chapter 6. Random walk and stochastic heat equation reviewed -- 6.1. Modification of the Local Limit Theorem
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|a 6.2. Approximations of the classical heat equation solution -- 6.3. Euler method for the stochastic heat equation -- 6.4. Convergence of interpolation of the Euler method -- 6.5. Euler method with initial value condition and no external noise -- Chapter 7. Limit of the natural Brownian motion on a rhombus grid -- 7.1. Natural Brownian motion on a rhombus grid -- 7.2. Network of Brownian bridges -- 7.3. The main result -- Part 3 . Processes on general and random time-like graphs -- Chapter 8. Non-simple TLG's -- 8.1. New definitions -- 8.2. Embedding TLG's into simple TLG's -- 8.3. TLG** family
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|a Chapter 9. Processes on non-simple TLG's -- 9.1. Processes on TLG** -- 9.2. Properties of constructed processes -- 9.3. Properties for Markov family \cM -- 9.4. Processes on time-like trees -- Chapter 10. Galton-Watson time-like trees and the Branching Markov processes -- 10.1. TLG's with an infinite number of vertices -- 10.2. Galton -Watson time-like tree -- 10.3. Processes on TLG**'s with infinite number of vertices -- 10.4. Natural \cP-Markov process -- 10.5. Branching \cP-Markov process -- Open questions and appendix -- Chapter 11. Open questions -- 11.1. Construction of process on all TLG's
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|a 11.2. Reconstruction of TLG's based on the process
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|a 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 resul.
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|a Online resource; title from digital title page (viewed on January 30, 2020).
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|a Includes bibliographical references (pages 167-168) and index.
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|a Distribution (Probability theory)
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|a distribution (statistics-related concept)
|2 aat
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|a Distribución (Teoría de probabilidades)
|2 embne
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|a Distribution (Probability theory)
|2 fast
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| 758 |
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|i has work:
|a Time-like graphical models (Text)
|1 https://id.oclc.org/worldcat/entity/E39PCGCPrDT6XFvg9GpR8p7HQ3
|4 https://id.oclc.org/worldcat/ontology/hasWork
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| 776 |
0 |
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|i Print version:
|a Tadić, Tvrtko.
|t Time-Like Graphical Models.
|d Providence : American Mathematical Society, ©2019
|z 9781470436858
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| 830 |
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0 |
|a Memoirs of the American Mathematical Society ;
|v no. 1262.
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| 856 |
4 |
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|u https://ebookcentral.proquest.com/lib/holycrosscollege-ebooks/detail.action?docID=5990834
|y Click for online access
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|a EBC-AC
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|a 92
|b HCD
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