Synchronization of mobile oscillators occurs in diverse contexts, from physical, chemical, biological to engineered systems. During vertebrate embryogenesis, the body segments form from a group of mobile cells that oscillate, interacting with neighbors via signaling to produce rhythmic gene expression patterns. Gradients in both oscillation frequency and cell mobility extend across this unsegmented tissue, and waves of gene expression travel through the tissue to create segment boundaries. While cell mobility can help cells to synchronize oscillations, it can also cause local defects in patterns, affecting segment formation. In this work, we propose a framework to describe how fluctuations caused by local mobility impact on synchronization and pattern stability. We use a statistical approach to describe these mobile oscillators, and formulate a Chapman-Kolmogorov equation for a probability density. We use this formulation to derive diffusion equations that connect local fluctuations to global synchronization in a uniform group of oscillators. We show how, when mobility is high, the system reaches a mean field regime where all oscillators behave as if they were coupled to all the rest. We then extend the analysis to non-uniform systems, to account for gradients present in the vertebrate segmenting tissue. In this extended framework, we link pattern stability to mobility, coupling, and pattern wavelength. This framework can be applied to other systems involving mobile oscillators, and more generally to pattern formation in the presence of mobility.