Importance sampling for maxima on trees

We study the all-time supremum of perturbed branching random walk, known to be endogenous solution high-order Lindley equation: W = D max Y , 1 ≤ i N ( + X ) where { } are independent copies vector taking values in R × ∞ . Under Kesten assumptions, this satisfies P > t ∼ H e − α → 0 solves Cramér–Lundberg equation E ∑ This paper establishes tail asymptotics by using forward iterations map defining fixed-point combined with a change measure along randomly chosen path. new approach provides an explicit representation constant and gives rise unbiased strongly efficient estimators for rare event probabilities