Title: Driving an Ornstein--Uhlenbeck Process to Desired First-Passage Time Statistics,
Abstract: First-passage time (FPT) of an Ornstein-Uhlenbeck (OU) process is of immense
interest in a variety of contexts. This paper considers an OU process with two
boundaries, one of which is absorbing while the other one could be either
reflecting or absorbing, and studies the control strategies that can lead to
desired FPT moments. Our analysis shows that the FPT distribution of an OU
process is scale invariant with respect to the drift parameter, i.e., the drift
parameter just controls the mean FPT and doesn't affect the shape of the
distribution. This allows to independently control the mean and coefficient of
variation (CV) of the FPT. We show that that increasing the threshold may
increase or decrease CV of the FPT, depending upon whether or not one of the
threshold is reflecting. We also explore the effect of control parameters on
the FPT distribution, and find parameters that minimize the distance between
the FPT distribution and a desired distribution.