Large Deviations for Controlled Branching Processes: Random Slopes, Harmonic Moments, and Transfer Principles
Let \(\{X_n:n\ge0\}\) be a controlled branching process with controls \(\phi_n\), and let \(N_n=\phi_n(X_n)\) be its progenitor count. We study large deviations of \(X_{n+1}/N_n\), \(N_n/X_n\), and \(X_{n+1}/X_n\), on their natural positive-denominator events, in supercritical and critical regimes. We treat generation-...