Large deviations for a Poisson random indexed branching process

Large deviations for Lotka-Nagaev estimator of a randomly indexed branching process

“…In [7], we gave the error bound in asymptotic normality. The large deviations in the Shröder case were given in [8], where the rate function I(x) is deferent from the Böttcher case for small positive x. Similar results for branching process indexed by a renewal process were done in [9] and [10].…”

Deviations for Jumping Times of a Branching Process Indexed by a Poisson Process

“…In Böttcher case, it was proved in [3] that log have similar asymptotic results to the Poisson process { }. But differences appeared in Shröder case; see [4]. For subcritical and critical PRIBP, one can see [5,6] for details.…”

Controlled branching processes with continuous time

“…BGW branching processes subordinated by a general renewal process were introduced in [16] and [21] (critical case) and in [14] and [18] (non-critical cases). Large deviation problems for a Poisson random indexed BGW branching process were considered in [5], [6], and [9]. Large and moderate deviations for a class of renewal random indexed BGW branching processes were studied in [7] and [8].…”