# Research

*"An approximate answer to the right problem is worth a good deal more than an exact answer to an approximate problem."*John Tukey.

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)

*Submitted*(2024)

*Preprint*(2023)

*Preprint*(2023)

*Submitted*(2023)

*Stochastic Process. Appl.*, to appear (2024)

*Submitted*(2022)

*Submitted*(2021)

*Submitted*(2021)

*ACM Trans. Model. Comput. Simul.*, 32(2):1-25, 2022.

*Stochastic Process. Appl.*, 145:143–164 2022.

*Ann. Appl. Probab.,*31(6):2811–2843, 2021.

*Potential Anal.*, 2021

*Monte Carlo and Quasi-Monte Carlo Methods 2018*, Springer Proceedings in Mathematics & Statistics, vol 324, 2020.

*Appl. Math. Optim.,*78(1), 103--144, (2018).

*J. Appl. Probab.,*54(2), 490--506, (2017).

*J. Chem. Phys.,*146, 134111 (2017).

*Stochastic Process. Appl.*, 126(1), 138--170 (2016).

*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**

*[Poster presentation]*

*[Poster presentation]*

**Meetings and summer schools**

- WASP Winter Conference 2020, Linköping, January 14-15, 2020.
- Winter Simulation Conference 2018, Dec 9-12, 2018, Gothenburg, Sweden.
- Seminar on Stochastic Processes 2018, ICERM, May 9-12, 2018.
- Monte Carlo Methods for Rare Events, Brown University, June, 2014.
- Charles River Lectures on Probability and Related Topics, Harvard University, October 17, 2014.
- Extremes in Space and Time - Ph.D. course and workshop, May 27-31, 2013, Copenhagen, Denmark.
- PDE and Mathematical Finance, June 10-13 2013, Stockholm, Sweden.
- Computational Challenges in Probability (semester program at ICERM), October 12-December 9, 2012, Providence, RI.
- INFORMS Applied Probability Society Conference, July 6-8, 2011, Stockholm, Sweden.
- Recent developments in mathematical finance, May 9-10, 2011, Stockholm, Sweden.
- IMS 73rd Annual Meeting, August 9-13, 2010, Gothenburg, Sweden.
- 6th International Conference on Levy Processes: Satellite Summer School, July 22-24, 2010, Braunschweig, Germany.