The randomized first-hitting problem of continuously time-changed Brownian motion
Summary: Let \(X(t)\) be a continuously time-changed Brownian motion starting from a random position \(\eta\), \(S(t)\) a given continuous, increasing boundary, with \(S(0) \geq 0\), \(P(\eta \geq S(0)) = 1\), and \(F\) an assigned distribution function. We study the inverse first-passage time problem for \(X(t)\), which consists in finding the distribution of \(\eta\) such that the first-passage time of \(X(t)\) below \(S(t)\) has distribution \(F\), generalizing the results, valid in the case when \(S(t)\) is a straight line. Some explicit examples are reported.
scientific article; zbMATH DE number 6994622
scientific article