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 . We construct and give asymptotic results for two different arrangements of inert particles and Brownian particles, and construct the analogous process in higher dimensions.
"Processes with inert drift." Electron. J. Probab. 12 1509 - 1546, 2007. https://doi.org/10.1214/EJP.v12-465