Controlled wear processes: modeling-optimal control

Wear processes modeled by a scalar Ito equation cannot have increasing paths unless the Ito equation is really a deterministic ordinary differential equation. However, vector Ito equations whose first component is just an ordinary differential equation with positive derivative yield a stochastic process whose first component has continuous increasing paths. Thus it is claimed that if Ito equations are used to model wear processes, they must always have a particular form. Control problems are set up for these types of wear models, and an explicit solution is obtained in a special case