math 5016 Spring 2020


Sasha Teplyaev 

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.



plan math 5016 2020


discussion 2020-01-27:
A celebration of Dynkin’s formula Probabilistic interpretations for ODE’s
Tommi Sottinen
University of Vaasa, Finland

Optional stopping theorem

Dynkin’s formula

Itô’s lemma — Itô formula

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

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)








diagram1, diagram2, diagram3 by  Zhi-Ming Ma and Michael Röckner from
Introduction to the Theory of (Non-Symmetric) Dirichlet Forms Springer 1992