Detecting origins of subdiffusion:P-variation test for confined systems

In this paper, we propose a method to distinguish between mechanisms leading to single molecule subdiffusion in confinement. We show that the method of p-variation, introduced in the recent paper M. Magdziarz, Phys. Rev. Lett. 103, 180602 (2009), can be successfully applied also for confined systems. We propose a test which allows distinguishing between heavy-tailed continuous-time random walk and fractional Brownian motion in the presence of binding potentials and reflecting boundaries. We apply our test to the experimental data describing motion of mRNA molecules inside E. coli cells. The results of the test show that it is more likely that fractional Brownian motion is the underlying process.