We construct a stochastic process whose drift is a function of the process's local time at a reflecting barrier. The process arose as a model of the interactions of a Brownian particle and an inert particle in a paper by Knight [7]. We construct and give asymptotic results for two different arrangements of inert particles and Brownian particles, and construct the analogous process in higher dimensions.
Electron. J. Probab.
12:
1509-1546
(2007).
DOI: 10.1214/EJP.v12-465