My research is mainly on the long-time behavior of branching diffusion processes with periodic diffusion and branching rates. We study the asymptotic behavior of the associated heat kernels in periodic domains using probabilistic techniques. I have also worked on discrete multi-type branching processes and their limiting behavior.
My advisor is Dr. Leonid Koralov .Publications
- D.Dolgopyat, P. Hebbar, L. Koralov, M. Perlman, "Multi-type branching processes with time-dependent branching rates", To appear in Journal of Applied Probability.
- P. Hebbar, J. Nolen, "The Asymptotics of Solutions to Parabolic PDEs with Periodic Coefficients", preprint.
- P. Hebbar, K. Fernando, "Asymptotic Expansions for Large Deviations with applications to stochastic differential equations", in preparation.
- "Multi-type branching processes with time-dependent branching rates"(pdf) , Workshop on Dynamical Systems and Related Topics, University of Maryland, College Park, USA (March 31 - April 2, 2017).
- "Multi-type branching processes with time-dependent branching rates", GWU-SIAM Conference on Applied Mathematics, George Washington University, Washington D.C, USA (April 29, 2017).
- "Asymptotics of some classes of SDE's in the Large Deviation Domain"(Poseter pdf) , Poster talk at the Seminar on Stochastic Processes, Brown University, Providence, USA (May 10, 2018).