# Skew Brownian motion with dry friction: The Pugachev-Sveshnikov approach

## TL;DR

This paper studies a generalized skew Brownian motion model incorporating dry friction, analyzing its probability distribution and occupation time using the Pugachev-Sveshnikov approach, with applications across physics and mathematics.

## Contribution

It introduces a comprehensive analysis of skew Brownian motion with dry friction using the Pugachev-Sveshnikov method, extending existing models in stochastic processes.

## Key findings

- Derived the probability distribution of the process.
- Analyzed the occupation time on the positive half line.
- Provided insights into the process's behavior under dry friction.

## Abstract

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.