## Research

I am a probabilist exploring the foundations of computational mathematics and data science. My research thus lies at the intersection of probability theory, mathematical statistics and applied mathematics. I am interested in further developing the theoretical framework associated with real-world problems from, e.g., physics, computer science, finance etc. Aside from theoretical questions in probability I have a particular interest in problems at the interface of computational probability and statistics.

Although I have a general interest in all of probability theory and much of what is categorized as applied mathematics, my current primary interests are: large deviations, stochastic numerical methods, empirical processes, mathematical statistics stochastic processes, random dynamical systems.

My research is partially supported by the NSF (DMS-1317199).

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

Co-authors: Amarjit Budhiraja, Boualem Djehiche, Jim Doll, Paul Dupuis ,Henrik Hult.

My Erdos number is 4

### Publications and preprints

- A. Budhiraja, P. Nyquist (2015). Large deviations for multidimensional state-dependent shot noise processes.
*J. Appl. Probab.*, 52(4), 1097--1114. - H. Hult, P. Nyquist (2016). Large deviations for weighted empirical measures from importance sampling .
*Stochastic Process. Appl.*, 126(1), 138--170. - B. Djehiche, H. Hult, P. Nyquist (2015). Min-max representations of viscosity solutions of Hamilton-Jacobi equations with applications in rare-event simulation.
*Math. Oper. Res.,*accepted with revision (30 pp.). - P. Nyquist (2015). Moderate deviation principles for importance sampling estimators of risk measures.
*Submitted (22 pp.).* - J.D. Doll, P. Dupuis, P. Nyquist (2016). A large deviation analysis of certain qualitative properties of parallel tempering and infinite swapping algorithms.
*Submitted (49 pp.).* - B. Djehiche, H. Hult, P. Nyquist (2016). Efficient importance sampling for a credit risk model.
*Preprint available upon request (23 pp.).*

### Some work in progress

- P. Dupuis, P. Nyquist. A variational characterization of heavy-tailed large deviations.

- P. Dupuis, P. Nyquist. Low-temperature limit of risk-sensitive functionals with respect to Gibbs measures: Finite state approximations.

- Efficient importance sampling for shot noise processes.

- Large deviations for random graphs using weak convergence methods.

### 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.

### Upcoming talks, professional travel and meetings

- 2016 IISA Conference, August 18-21, 2016, Corsville, OR.
- CMStatistics 2016, December 9-11, 2016, Seville, Spain.

During the academic year I (try to) attend the probability and statistics seminars at MIT and BU.

### Previous talks and presentations

- 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.

"Large deviations for weighted empirical measures arising in importance sampling". - 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.
- 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

- 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.