Research interests:

My research is in probability theory and its connections to data-science. Some specific areas of interest include

• Statistical learning theory with special interest in inference of stochastic dynamical systems, stochastic methods in computing, statistical algorithms

• Limit theorems with special interest in large deviation analysis; their applications to statistics and numerical methods

• Multiscale stochastic systems, averaging principle and applications to model reduction techniques

Grants:

• Travel support for Mathematicians, Simons Foundation, September 1, 2023

• NSF DMS - 2246815, August 15, 2023 - July 31, 2026

• NSF DMS - 1855788, July 1, 2019- June 30, 2023

• LA Board of Regents, July 1, 2016-June 30, 2019

Selected Works: 

• Optimal learning via moderate deviations theory. Co-author: T. Sutter. Preprint, 2023. arXiv 2305.14496

• Infinite-dimensional optimization and Bayesian nonparametric learning of stochastic differential equations. Co-authors: R. Mitra, J. Zhou. Journal of Machine Learning Research, 24(159),1−39, 2023. arXiv:2205.15368

• Moment stability of stochastic processes with applications to control systems. Co-author: D. Chatterjee. Mathematical Control and Related Fields, 2023.  arXiv:2206.00200

• Inhomogeneous functionals and approximations of invariant distribution of ergodic diffusions: Central limit theorem and moderate deviation asymptotics. Co-author: P. Sundar. Stochastic Processes and their Applications, 133, 74-110, 2021. arXIv:1805.06388

• Large Deviations for Small Noise Diffusions in a Fast Markovian Environment.  Co-authors: A. Budhiraja, P. Dupuis. Electron. J. Probab., Vol. 23 (2018), paper 112, pp 33.  arXiv:1705.0294.

• Large deviation principle for stochastic integrals and stochastic differential equations driven by  infinite-dimensional  semimartingales. Stochastic Processes and their Applications,  128 (7), 2179 - 2227, 2018. arXiv:1101.5515.

• A variational approach to path estimation and parameter inference of hidden diffusion processes. Co-authors: T.Sutter, H.Koeppl. Journal of Machine Learning Research, 17(190), 1 - 37, 2016.  arXiv:1508.00506.

•  Moderate Deviation Principles for Stochastic Differential Equations with Jumps. Co-authors: A. Budhiraja, P. Dupuis. Annals of Probability, Vol. 44, No. 3, 1723 -1775, 2016. arXiv:1401.7316.

•  Efficient simulation of multiscale reaction networks: A multilevel partitioning approach. Co-authors: D. Altintan, H.Koeppl. Proceedings of ACC, 2016, pages 6073 - 6078, Print ISBN: 978-1-4673-8683-8.

•  Error bound and simulation algorithm for piecewise deterministic approximations of stochastic reaction systems. Co-authors: D. Altintan, H.Koeppl. Proceedings of ACC, 2015, pages 787 - 792, Print ISBN: 978-1-4799-8685-9.

•  Jump-Diffusion Approximation of Stochastic Reaction Dynamics: Error bounds and Algorithms. Co-authors: D. Altintan, H .Koeppl. SIAM: Multiscale Modeling and Simulation. 13(4), 1390 - 1419, 2015. arXiv:1409.4303.

•  Markov chain aggregation and its applications to combinatorial reaction networks.  Co-authors: T. Petrov, H. Koeppl. Journal of Mathematical Biology, Vol. 69, Issue 3, pp 767-797, 2014. arXiv:1303.4532.

•  Wong-Zakai type convergence  in infinite dimensions. Electron. J. Probab. Vol. 18, No. 31, 34 pp, 2013.

•  Hybrid spatial Gillespie and particle tracking simulation. Co-authors: M. Klann, H. Koeppl. Bioinformatics, Vol. 28, No. 18, pp. i549-i555, 2012.

•  Model Decomposition and Stochastic Fragments. Co-authors: T. Petrov, H. Koeppl. Electronic Notes in Theoretical Computer Science, Vol. 284, 105-124, 2012.

•  Accounting for extrinsic variability in the estimation of stochastic rate constants.  Co-authors: H. Koeppl, C. Zechner, S. Pelet, M. Peter. International Journal of Robust and Nonlinear Control, Vol. 22, No. 10, 1103 - 1119, 2012.

•  Deterministic characterization of phase noise in biomolecular oscillators. Co-authors: H. Koeppl, M. Hafner, A. Ganguly, A. Mehrotra. Physical Biology,  Vol. 8, No. 5, 2011.

•  Error analysis of tau-leap simulation methods. Co-authors: D. F. Anderson, T. G. Kurtz.  Annals of Applied Probability, Vol. 21, No. 6, 2226 - 2262, 2011. arXiv:0909.4790v1.