The advent of single molecule microscopy has revolutionized biological investigations by providing a powerful tool for the study of intercellular and intracellular trafficking processes of protein molecules which was not available before through conventional microscopy. In practice, pixelated detectors are used to acquire the images of fluorescently labeled objects moving in cellular environments. Then, the acquired fluorescence microscopy images contain the numbers of the photons detected in each pixel, during an exposure time interval. Moreover, instead of having the exact locations of detection of the photons, we only know the pixel areas in which the photons impact the detector. These challenges make the analysis of single molecule trajectories, from pixelated images, a complex problem. Here, we investigate the effect of pixelation on the parameter estimation of single molecule trajectories. In particular, we develop a stochastic framework to calculate the maximum likelihood estimates of the parameters of a stochastic differential equation that describes the motion of the molecule in living cells. We also calculate the Fisher information matrix for this parameter estimation problem. The analytical results are complicated through the fact that the observation process in a microscope prohibits the use of standard Kalman filter type approaches. The analytical framework presented here is illustrated with examples of low photon count scenarios for which we rely on Monte Carlo methods to compute the associated probability distributions.