SOME REMARKS ON THE MAXIMUM OF A ONE-DIMENSIONALDIFFUSION PROCESS
Mario Abundo
Abstract: For a certain class of one-dimensional diffusions
we study the distribution of
and the distribution of the
first instant at which attains
the maximum by reducing to
Brownian motion. Moreover, for
fixed or random, we study the asymptotics of threshold crossing probability, i.e. the rate of decay
of as
goes
to infinity. Some examples are also reported.