An inverse first-passage problem revisited: the case of fractional Brownian motion, and time-changed Brownian motion. Issue 5 (3rd September 2019) - Abundo, Mario
Abstract: We revisit an inverse first-passage time (IFPT) problem, in the cases of fractional Brownian motion, and time-changed Brownian motion. Let X ( t ) be a one dimensional continuous stochastic process starting from a random position η, and let S ( t ) be an assigned continuous boundary, such that P ( η ≥ S ( 0 ) ) = 1, and F an assigned distribution function. The IFPT problem here considered consists in finding the distribution of η such that the first-passage time of X ( t ) below S ( t ) has distribution F . We study this IFPT problem for fractional Brownian motion and a constant boundary S ( t ) = S ; we also obtain some extension to other Gaussian processes, for one, or two, time-dependent boundaries.