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}
}