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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.
Keywords: Skew Brownian motion, Pugachev−Sveshnikov equation, dry friction, local time |
full paper (pdf, 912 Kb)