We investigate the large deviation probabilities of first passage times (FPT) of discrete-time supercritical non-lattice branching random walks (BRWs) in Rᵈ where d 1. The FPT refers to the first time the BRW enters a ball of radius one with a distance x from the origin, conditioned upon the process's survival. Furthermore, we apply the spine decomposition technique to construct an asymptotically optimal polynomial-time algorithm for computing the lower large deviation probabilities of the FPT. The accuracy of our algorithm is also verified numerically. Our analysis not only provides a deeper theoretical understanding of these stochastic processes but also offers new insights into the microstructural features that are key to characterizing the strength of polymers.
Blanchet et al. (Wed,) studied this question.