Publications of Pratima Hebbar

%% Papers Published   
@article{fds352643,
   Author = {Fernando, K and Hebbar, P},
   Title = {Higher order asymptotics for large deviations-Part
             II},
   Journal = {Stochastics and Dynamics},
   Volume = {21},
   Number = {5},
   Year = {2021},
   Month = {August},
   Abstract = {We obtain asymptotic expansions for the large deviation
             principle (LDP) for continuous time stochastic processes
             with weakly-dependent increments. As a key example, we show
             that additive functionals of solutions of stochastic
             differential equations (SDEs) satisfying Hörmander
             condition on a d-dimensional compact manifold admit these
             asymptotic expansions of all orders.},
   Doi = {10.1142/S0219493721500258},
   Key = {fds352643}
}

@article{fds348751,
   Author = {Fernando, K and Hebbar, P},
   Title = {Higher order asymptotics for large deviations - Part
             i},
   Journal = {Asymptotic Analysis},
   Volume = {121},
   Number = {3-4},
   Pages = {219-257},
   Publisher = {IOS Press},
   Year = {2021},
   Month = {January},
   Abstract = {For sequences of non-lattice weakly dependent random
             variables, we obtain asymptotic expansions for Large
             Deviation Principles. These expansions, commonly referred to
             as strong large deviation results, are in the spirit of
             Edgeworth Expansions for the Central Limit Theorem. We show
             that the results are applicable to Diophantine iid
             sequences, finite state Markov chains, strongly ergodic
             Markov chains and Birkhoff sums of smooth expanding maps &
             subshifts of finite type.},
   Doi = {10.3233/ASY-201602},
   Key = {fds348751}
}

@article{fds350370,
   Author = {Hebbar, P},
   Title = {Differential Equations For Scientists and
             Engineers},
   Journal = {Physics Today},
   Volume = {73},
   Number = {7},
   Pages = {54-55},
   Publisher = {AIP Publishing},
   Year = {2020},
   Month = {July},
   Doi = {10.1063/pt.3.4525},
   Key = {fds350370}
}

@article{fds353260,
   Author = {Hebbar, P and Koralov, L and Nolen, J},
   Title = {Asymptotic behavior of branching diffusion processes in
             periodic media},
   Journal = {Electronic Journal of Probability},
   Volume = {25},
   Pages = {1-40},
   Year = {2020},
   Month = {January},
   Abstract = {We study the asymptotic behavior of branching diffusion
             processes in periodic media. For a super-critical branching
             process, we distinguish two types of behavior for the
             normalized number of particles in a bounded domain,
             depending on the distance of the domain from the region
             where the bulk of the particles is located. At distances
             that grow linearly in time, we observe intermittency (i.e.,
             the k-th moment dominates the k-th power of the first moment
             for some k), while, at distances that grow sub-linearly in
             time, we show that all the moments converge. A key
             ingredient in our analysis is a sharp estimate of the
             transition kernel for the branching process, valid up to
             linear in time distances from the location of the initial
             particle.},
   Doi = {10.1214/20-EJP527},
   Key = {fds353260}
}

@article{fds346355,
   Author = {Dolgopyat, D and Hebbar, P and Koralov, L and Perlman,
             M},
   Title = {Multi-type branching processes with time-dependent branching
             rates},
   Journal = {Journal of Applied Probability},
   Volume = {55},
   Number = {3},
   Pages = {701-727},
   Year = {2018},
   Month = {September},
   Abstract = {Under mild nondegeneracy assumptions on branching rates in
             each generation, we provide a criterion for almost sure
             extinction of a multi-type branching process with
             time-dependent branching rates. We also provide a criterion
             for the total number of particles (conditioned on survival
             and divided by the expectation of the resulting random
             variable) to approach an exponential random variable as time
             goes to ∞.},
   Doi = {10.1017/jpr.2018.46},
   Key = {fds346355}
}