Processes with inert drift
Abstract (summary)
The work in this dissertation consists of four main parts. The first part generalizes the results of Frank Knight [Kni01] about the existence and uniqueness of processes with an inert drift term.
The second part extends the work in the first part to domains in [special characters omitted] for d ≥ 2. The class of domains includes C2 domains.
The third part uses results from the first part to analyze the case where a Brownian particle is confined to an interval bounded by two inert particles a fixed distance apart. It is shown that the limit under resealing is an Ornstein-Uhlenbeck process.
The final part analyzes the case where two Brownian particles contain a single inert particle. It is shown that the limit under resealing is the two-dimensional Bessel process.