  The Caughey-Dieness process, also known as the Brownian motion with two
valued drift, is used in theoretical physics as an advanced model of the
Brownian particle velocity if the resistant force is assumed to be dry
friction. This process also appears in many other fields, such as applied
physics, mechanics, astrophysics, and pure mathematics. In the present paper we
are concerned with a more general process, skew Brownian motion with dry
friction. The probability distribution of the process itself and of its
occupation time on the positive half line are studied. The approach based on
the Pugachev-Sveshnikov equation is used.
