2007/10/18 by Peter Mörters, Marcel Ortgiese, Morters, Peter +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #60F10 (Primary) #60J55 (Secondary) #60J65 #60J80 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.0710.3493
openalex publication_date 2007/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the first part of this paper we give easy and intuitive proofs for the small value probabilities of the martingale limit of a supercritical Galton-Watson process in both the Schröder and the Böttcher case. These results are well-known, but the most cited proofs rely on generating function arguments which are hard to transfer to other settings. In the second part we show that the strategy underlying our proofs can be used in the quite different context of self-intersections of stochastic processes. Solving a problem posed by Wenbo Li, we find the small value probabilities for intersection local times of several Brownian motions, as well as for self-intersection local times of a single Brownian motion.