MATH 5016 — Topics in Probability: Discretization of continuous processes — Spring 2020
(Math 5016 Syllabus Spring 2020)
A paper to consider: Evarist Giné and Vladimir Koltchinskii. “Empirical graph Laplacian approximation of Laplace-Beltrami operators: Large sample results.” High dimensional probability (pp 238-259) Institute of Mathematical Statistics, 2006.
discussion 2020-01-27:
A celebration of Dynkin’s formula Probabilistic interpretations for ODE’s
Tommi Sottinen
University of Vaasa, Finland
Ann. Probab. Volume 1, Number 4 (1973), 570-579.
A Generalization of Dynkin’s Identity and Some Applications
Krishna B. Athreya and Thomas G. Kurtz
Intro lectures on Dynkin’s formula
Heat kernels on the unit circle and on intervals
Ideas about symmetric processes (2020-02-07):
Symmetric (continuous time) Markov processes on a finite or countable state space, detailed balanced condition:
A detailed balanced reaction network is sufficient but not necessary for its Markov chain to be detailed balanced arXiv:1312.4196 Badal Joshi DCDS-B 2015, 20(4): 1077-1105. doi: 10.3934/dcdsb.2015.20.1077
Dirichlet forms and stochastic completeness of graphs and subgraphs Matthias Keller, Daniel Lenz arXiv:1312.4196
- Stochastic Completeness of Graphs Radoslaw K. Wojciechowski arXiv:0712.1570
- Stochastic completeness of Markov processes Alexander Grigor’yan
Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35) Zhenqing Chen and Masatoshi Fukushima
Rick Durrett Probability: Theory and Examples (Section “Stationary Measures”) 4th edition or 5th edition (free)
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2020-04-03:
diagram1, diagram2, diagram3 by Zhi-Ming Ma and Michael Röckner from
Introduction to the Theory of (Non-Symmetric) Dirichlet Forms Springer 1992
2020-04-20:
