Moment generating function of a first hitting place for the integrated Ornstein-Uhlenbeck process
An explicit expression for the moment generating function of x(T) is obtained, when \(y\geq v\geq 0\), where \(T=\min \{t:\) \(y(t)=v\}\), y(t) is an Ornstein-Uhlenbeck process with \(y(0)=y\) and \(x(t)=x+\int^{t}_{0}y(s)ds\), and for the characteristic function of x(T) when y(0)\(\leq v\) \((v>0).\) The expected value of x(T) turns out to be the same in both cases considered.
scientific article; zbMATH DE number 4107868