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. Publications and preprints reverse chronological order. Nyquist Large deviations and design of efficient importance sampling algorithms. Doctoral thesis. Large deviations for weighted empirical measures and processes arising in importance sampling.
Licentiate thesis. Research "An approximate answer to the right problem is worth a good deal more than an exact answer to an approximate problem. My Erdos number is 4 Publications and preprints reverse chronological order H. Hult, A. Lindhe, P. Nyquist, G. A weak convergence approach to large deviations for stochastic approximations. Preprint Jain, S. Juneja, P. Nyquist, S. A deep learning approach for rare event simulation for diffusion processes.
Nilsson, A. Sameddar, S. Madireddy, P. ICML Milinanni, P. On the large deviation principle for Metropolis-Hastings Markov Chains: the Lyapunov function condition and examples. Submitted On the projected Aubry set of the rate function associated with large deviations for stochastic approximations. A large deviation principle for the empirical measures of Metropolis-Hastings chains.
