A factorisation of diffusion measure and finite sample path constructions
The authors give a novel construction of the Brownian bridge with known range for its extrema. On the basis of this, they introduce decompositions of diffusion measure and, further, construct an algorithm for the exact simulation of diffusion sample paths and of diffusion hitting times of smooth boundaries. In comparison with \textit{A.~Beskos} and \textit{G.~O.~Roberts} [Ann. Appl. Probab. 15, No.~4, 2422--2444 (2005; Zbl 1101.60060)] and with \textit{A.~Beskos}, \textit{O.~Papaspiliopoulos}, and \textit{G.~O.~Roberts} [Bernoulli 12, No.~6, 1077--1098 (2006; Zbl 1129.60073)], there are now: ``probabilistic results on the absolute maximum of Brownian paths and the maximum of Bessel process paths; a novel rejection sampling algorithm for the simulation of Brownian paths with known range'' (from the introduction).
scientific article; zbMATH DE number 5314364