DESCRIPTION: This is a learning/reading seminar on stochastic systems. Faculty, postdocs, visiting scholars and graduate students will take turns presenting topics and research papers on stochastic systems arising in applications. Potential areas of application include biology, telecommunications, operations management, neuroscience and finance.

This seminar will run in Winter and Spring 2019. It will meet at 3-3.50pm on Thursdays in AP&M 7421 (there will be no seminar on Thursday, February 21 nor March 7, 2019). On Thursday, February 7, instead of the seminar, there will be a special lecture by Professor Simon Tavare at 5pm in the Natural Sciences Building Auditorium. Please click here for more information and to register to attend.

In Winter and Spring 2019, the topic will focus on stochastic systems in biology and telecommunications. However, the mathematical tools learned can apply to other applications. To begin with, Professor Tom Kurtz will give some lectures on stochastic models of biochemical reaction networks, including mathematical and probabilistic techniques for proving scaling limits. Subsequently, various research papers on stochastic modeling and control of biological and other systems will be studied.

A new reading list will be provided for the seminar. (To get a flavor of a similar past seminar, see the past seminar link below or the topic links above that.)

The seminar will meet once a week for an hour. PhD students can sign up for one unit of Math 288C. (Suitable background is having taken the equivalent of Math 280ABC.)


  • Thursday, January 17, 24, 31, 3pm, AP&M 7421.
    Professor Tom Kurtz, University of Wisconsin, Madison.

  • Thursday, January 17, 2019: Generators, martingale problems, and stochastic equations, Tom Kurtz. Click here for slides from this lecture.
  • Thursday, January 24, 2019: Controlled and constrained martingale problems, Tom Kurtz.
  • Thursday, January 31, 2019: Averaging fast subsystems in chemical network models, Tom Kurtz. For notes associated with this lecture, click here.
  • Thursday, February 7, 5pm, Natural Sciences Building Auditorium. Please note special time and location.
    Professor Simon Tavare, Murray and Adylin Rosenblatt Endowed Lecture in Applied Mathematics.

  • Thursday, February 28, 3pm, AP&M 7421, Yingjia Fu, On the paper: Weina Wang, Siva Theja Magul uri, R Srikant, Lei Ying, Heavy-Traffic Insensitive Bounds for Weighted Proportionally Fair Bandwidth Shar ing Policies, preprint, 2018.

    SPRING 2019

  • Thursday, April 18, 2019, 3pm. Jiaqi Liu. On "The combined effects of Feller diffusion and transcriptional/ translational bursting in simple gene networks" by Mateusz Falfus, Michael C. Mackney and Marta Tyran-Kaminska. Click here for a copy of the paper.

    SOME RECENT PAPERS (for 2019 seminar series)

    Biochemical Reaction Networks and Martingale Problems

  • See papers by Tom Kurtz by clicking here (Google scholar page).
  • For some background on stochastic models of biochemical reaction networks, see D. F. Anderson and T. G. Kurtz, Continuous time Markov chain models for chemical reaction networks, chapter in Design and Analysis of Biomolecular Circuits: Engineering Approaches to Systems and Synthetic Biology, H. Koeppl. et al. (eds.), Springer.
    For papers related to Professor Kurtz's lectures, see especially the following:
  • David F Anderson, Daniele Cappelletti, Masanori Koyama, Thomas G Kurtz, Non-explosivity of stochastically modeled reaction networks that are complex balanced, Bulletin of Mathematical Biology, 2018.
  • David F Anderson, Daniele Cappelletti, Thomas G Kurtz, Finite time distributions of stochastically modeled chemical systems with absolute concentration robustness, SIAM J on Applied Dynamical Systems, 2017.
  • Cristina Costantini and Thomas G. Kurtz, Viscosity methods giving uniqueness for martingale problems, Electronic J Probability, 2015.

  • Control and Adaptation in Biological Networks
  • Briat, Gupta and Khammash, Antithetic Integral Feedback Ensures Robust Perfect Adaptation in Noisy Biomolecular Networks, Cell Systems, 2016.
  • Corentin Briat, Ankit Gupta, Mustafa Khammash, Antithetic proportional-integral feedback for reduced variance and improved control performance of stochastic reaction networks, J. Royal Society Interface, 2018.
  • Ankit Gupta, Mustafa Khammash, Sensitivity analysis for multiscale stochastic reaction networks using hybrid approximations, preprint, 2018.

  • Overview of control in biological systems on the website of Prof Eduardo Sontag
  • Index to papers of Professor Eduardo Sontag.
  • D. Del Vecchio, Y. Qian, R.M Murray, and E.D. Sontag. Future systems and control research in synthetic biology. Annual Reviews in Control, 45:5-17, 2018.
  • E.D. Sontag. Examples of computation of exact moment dynamics for chemical reaction networks. In R. Tempo, S. Yurkovich, and P. Misra, editors, Emerging Applications of Control and Systems Theory, volume 473 of Lecture Notes in Control and Inform. Sci., pages 295-312. Springer-Verlag, Berlin, 2018.

  • Website of Professor Johan Paulsson on stochastics and decision making.
  • Laurent Potvin-Trottier, Nathan D. Lord, Glenn Vinnicombe and Johan Paulsson, Synchronous long-term oscillations in a synthetic gene circuit, Nature, 2016.
  • Hilfinger, A. ; Norman, T. M. ; Paulsson, J. Exploiting natural fluctuations to identify kinetic mechanisms in sparsely characterized systems. Cell Systems, 2016.
  • Potvin-Trottier, Luro, Paulsson, Microfluidics and single-cell microscopy to study stochastic processes in bacteria, Current Opinion in Microbiology, 2018.

  • Website of Professor Richard Murray.
  • X. Flora Meng, Ania-Ariadna Baetica, Vipul Singha, and Richard M. Murray, Recursively constructing analytic expressions for equilibrium distributions of stochastic biochemical reaction networks, J. Royal Society Interface, 2017.
  • Xinying Ren, Richard M Murray, Cooperation Enhances Robustness of Coexistence in Spatially Structured Consortia,

    Stochastic Models in Gene Networks

  • The combined effects of Feller diffusion and transcriptional/translational bursting in simple gene networks, Mateusz Falfus, Michael C. Mackey, and Marta Tyran-Kaminska, Preprint, 2019.

    Bandwidth Sharing Networks

  • Weina Wang, Siva Theja Maguluri, R Srikant, Lei Ying, Heavy-Traffic Insensitive Bounds for Weighted Proportionally Fair Bandwidth Sharing Policies, preprint, 2018.

    SOME SAMPLE PAPERS (from the 2005-06 seminar series)

  • Biology
  • Epidemics and Immunology
  • Finance
  • Neuroscience
  • Operations Management
  • Communications
  • 2005-06.

    Please address all enquiries concerning this seminar to Professor Williams at williams at math dot ucsd dot edu