Pak-Wing Fok University of Delaware
Title: Reconstructing the drift in a stochastic process from distributions of exit times
Consider a brownian particle diffusing in a potential well of unknown shape. Given the distribution of exit times, can one reconstruct the function form of the potential? This stochastic inverse problem has several applications in biology and biophysics. We show that while reliable reconstruction of gross attributes, such as the height and the width of the potential, can be easily achieved from a single exit time distribution, the reconstruction of finer structure is ill-conditioned. Furthermore, we show that reconstruction of more complicated potentials containing multiple minima can be achieved by simultaneously using two or more measured exit time distributions. For example, by changing the potential by known amounts, additional measured exit distributions render the problem less ill-conditioned.

©2010, Department of Mathematical Sciences
Last Modified: February 25, 2010