Tree-indexed processes: a high level crossing analysis
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Kelbert, M., & Suhov, Y. (2003). Tree-indexed processes: a high level crossing analysis. https://doi.org/10.1155/S1048953303000091
Consider a branching diffusion process on R1 starting at the origin. Take a high level u>0 and count the number R(u,n) of branches reaching u by generation n. Let Fk,n(u) be the probability P(R(u,n)<k),k=1,2,…. We study the limit limn→∞Fk,n(u)=Fk(u). More precisely, a natural equation for the probabilities Fk(u) is introduced and the structure of the set of solutions is analysed. We interpret Fk(u) as a potential ruin probability in the situation of a multiple choice of a decision taken at vertices of a logical tree . It is shown that, unlike the standard risk theory, the above equation has a manifold of solutions. Also an analogue of Lundberg's bound for branching diffusion is derived.
External DOI: https://doi.org/10.1155/S1048953303000091
This record's URL: https://www.repository.cam.ac.uk/handle/1810/266296
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