My research interest lie at the intersection of probability theory, mathematical statistics and applied mathematics. Lately I have been increasingly interested in the mathematical foundation of the analysis and modelling of complex data, and the interplay with ideas from physics. My main expertise is in probability theory, where I have focused on large deviations theory and stochastic numerical methods. Aside from theoretical questions in probability I have a particular interest in problems from computational probability and statistics. The mathematical tools I use come from areas such as probability, analysis, PDE theory, optimization, stochastic optimal control.

I have a general interest in all of probability theory and much of what is categorized as applied mathematics. Current interests include: large deviations, gradient flows and their generalisations, stochastic numerical methods, statistical learning theory, stochastic processes, random dynamical systems.

For questions or a more thorough description of my research feel free to send me an email. You can find most of my papers on the arXiv.

My Erdos number is 4

Publications and preprints (reverse chronological order)

  • H. Hult, A. Lindhe, P. Nyquist. On the projected Aubry set of the rate function associated with large deviations for stochastic approximations. Preprint (2023)
  • H. Hult, A. Lindhe, P. Nyquist, G.-J. Wu. A weak convergence approach to large deviations for stochastic approximations. Preprint (2023)
  • A. Kramer, F. Milinanni, P. Nyquist, A. Jauhiainen, O. Eriksson. UQSA -- An R-Package for Uncertainty Quantification and Sensitivity Analysis for Biochemical Reaction Network Models. Submitted (2023)
  • F. Milinanni, P. Nyquist. A large deviation principle for the empirical measures of Metropolis-Hastings chains. Submitted (2023)
  • V. Nilsson, P. Nyquist. A note on large deviations for interacting particle dynamics for finding mixed equilibria in zero-sum games. Submitted (2022)
  • O. Eriksson, F. Milinanni, A. Kramer, P. Nyquist. Sensitivity approximation by the Peano-Baker series. Submitted (2021)
  • B. Djehiche, H. Hult, P. Nyquist. Min-max representations of viscosity solutions of Hamilton-Jacobi equations. Submitted (2021)
  • B. Djehiche, H. Hult, P. Nyquist. Importance sampling for a simple Markovian intensity model using subsolutions. ACM Trans. Model. Comput. Simul., 32(2):1-25, 2022.
  • A. Budhiraja, P. Dupuis, P. Nyquist, G.-J. Wu. Quasistationary Distributions and Ergodic Control Problems Stochastic Process. Appl., 145:143–164 2022.
  • J. Birkens, P. Nyquist, M. Schlottke. Large deviations for the empirical measures of the zig-zag process. Ann. Appl. Probab., 31(6):2811–2843, 2021.
  • N. Gavish, P. Nyquist, M. A. Peletier. Large deviations and gradient flows for the Brownian one-dimensional hard-rod system. Potential Anal., 2021
  • H. Hult, P. Nyquist, C. Ringqvist. The infinite swapping algorithm for restricted Boltzmann machines. Monte Carlo and Quasi-Monte Carlo Methods 2018, Springer Proceedings in Mathematics & Statistics, vol 324, 2020.
  • J.D. Doll, P. Dupuis, P. Nyquist. A large deviation analysis of certain qualitative properties of parallel tempering and infinite swapping algorithms. Appl. Math. Optim., 78(1), 103--144, (2018).
  • P. Nyquist Moderate deviation principles for importance sampling estimators of risk measures. J. Appl. Probab., 54(2), 490--506, (2017).
  • J. Doll, P. Dupuis, P. Nyquist. Thermodynamic integration methods, infinite swapping and the calculation of generalized averages. J. Chem. Phys., 146, 134111 (2017).
  • H. Hult, P. Nyquist. Large deviations for weighted empirical measures from importance sampling . Stochastic Process. Appl., 126(1), 138--170 (2016).
  • A. Budhiraja, P. Nyquist Large deviations for multidimensional state-dependent shot noise processes. J. Appl. Probab., 52(4), 1097--1114 (2015).

    • Theses

    P. Nyquist (2014). Large deviations and design of efficient importance sampling algorithms. Doctoral thesis.

    P. Nyquist (2013). Large deviations for weighted empirical measures and processes arising in importance sampling. Licentiate thesis.

    Talks and presentations

  • IDEAS Seminar, UNC Chapel Hill, March 30, 2023.
  • Mini-symposium on interacting particles and mean-field limits, Department of Mathematics and Computer Science, TU Eindhoven. February 3, 2023.
  • New interfaces of stochastic analysis and rough paths, Banff, September 4–9, 2022.
  • Nordic Congress of Mathematicians 2020, Helsinki, August 18-21, 2022.
  • Mathematics for Complex Data, Stockholm, June, 2022.
  • INFORMS Annual Meeting 2021, Anaheim, CA, October 24–27, 2021.
  • Stochastic analysis of the neutron transport equations, Bath, September 16–17, 2021.
  • Non-reversible Markovian Monte Carlo, Lorentz Center, Leiden, August 2–6, 2021.
  • Extreme Value Analysis 2021, Edinburgh, June 28–July 2, 2021. (moved online)
  • RESIM 2020 (Plenary speaker), Paris, May 18-21, 2021.
  • Applied CATS seminar KTH, May 4, 2021.
  • Applied Math seminar, UMass Amherst, May 4, 2021.
  • Probability and statistics seminar, University of Kansas, April 28, 2021.
  • IEMS Seminar, Northwestern University, February 18, 2020.
  • Random Matrix Theory Seminar, KTH, February 11, 2020.
  • Probability Seminar, Division of Applied Mathematics, Brown University. November 14, 2019.
  • INFORMS Annual Meeting, Seattle, Oct. 20-23, 2019.
  • AIM Workshop: Deep learning and PDEs, American Institute of Mathematics, San Jose, Oct. 14-18, 2019.
  • Equadiff 2019, July 8-12, 2019, Leiden, Netherlands.
  • Extreme Value Analysis 2019, July 1-5, 2019, Zagreb, Croatia.
  • Finance and Stochastics seminar, Ecole Polytechnique/ENSTA/ENSAE, October 1, 2018, Paris, France.
  • Probability and Statistics seminar, TU Delft, September 24, 2018, Delft, Netherlands.
  • MCQMC 2018, July 1-6, 2018, Rennes, France.
  • 40th Conference on Stochastic Processes and Their Applications (SPA2018), June 11-15, 2018, Gothenburg, Sweden.
  • CASA Colloquium, Department of Mathematics and Computer Science, TU Eindhoven. February 28, 2018.
  • Mathematics Colloquium, Department of Mathematics, Aarhus University. December 5, 2017.
  • 39th Conference on Stochastic Processes and Their Applications (SPA2017), July 24-28, 2017, Moscow, Russia.
  • Operations Research Seminar, Department of Mathematics and Systems Analysis, Aalto University. May 22, 2017.
  • Mathematics Colloquium, Department of Mathematics, Aarhus University. January 16, 2017.
  • CMStatistics 2016, December 9-11, 2016, Seville, Spain.
  • KTH Probability Seminar, October 31, 2016, Stockholm, Sweden.
  • Mathematics Colloquium, School of Mathematics, University of Edinburgh. June 29, 2016.
  • Statistics Seminar, Department of Statistical Science, Duke University. April 6, 2016.
  • Young European Probabilists 13: Large deviations for interacting particle systems and partial differential equations, EURANDOM, March 7-11, 2016.
  • INFORMS Annual Meeting 2015, November 1-4, 2015, Philadelphia, PA.
  • Extreme Value Analysis Conference 2015, June 15-19, 2015, Ann Arbor, MI.
  • ISyE Seminar, School of Industrial and Systems Engineering, Georgia Tech. April 14, 2015.
  • Probability and Statistics Seminar, Department of Mathematics and Statistics, Boston University. February 19, 2015.
  • Probability Seminar, Division of Applied Mathematics, Brown University. December 9, 2014.
  • RESIM 2014, August 27-29, 2014, Amsterdam, Netherlands.
  • 59th World Statistics Congress, August 25-30, 2013, Hong Kong, China. .
  • 4th Northern Triangle Seminar, March 6-8, 2013, Helsinki, Finland.
  • Performance Analysis of Monte Carlo Methods, November 28-30, 2012, Providence, RI. [Poster presentation]
  • STOR Colloquia, University of North Carolina at Chapel Hill, November 14, 2012.
  • RESIM 2012, June 25-27, 2012, Trondheim, Norway.
  • INFORMS Simulation Society Research Workshop - Simulation in complex service systems, July 18-20, 2011, Montreal, Canada. [Poster presentation]
  • 13th Stockholm-Uppsala symposium, May 24, 2011, Uppsala University.
  • 3rd Northern Triangle Seminar, April 11-13, 2011, St. Petersburg, Russia. [Link]

    • Meetings and summer schools