Inference of hopping rates of anisotropic random walk on a 2D lattice via covariance-based estimators of diffusion parameters

Abstract: Traditionally, time-development of the mean square displacement has been employed to determine the diffusion coefficient from the trajectories of single particles. However, this approach is sensitive to the noise and the motion blur upon image acquisition. Recently, Vestergaard et al. has proposed a novel method based on the covariance between the shifted displacement series. This approach gives a more robust estimator of the diffusion coefficient of one-dimensional diffusion without bias, i.e., when mean velocity is zero. Here, we extend this approach to a potentially biased random walk on a two-dimensional lattice. First, we describe the relationship between the hopping rates to the eight adjacent sites and the time development of the higher-order moments of the stochastic two-dimensional displacements. Then, we derive the covariance-based estimators for these higher-order moments. Numerical simulations confirmed that the procedure presented here allows inference of the stochastic hopping rates from two-dimensional trajectory data with location error and motion blur.