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Molecular detection in real-time affinity-based biosensors relies on temporal sampling of the binding process in which target molecules are captured by their respective probes. The capturing process is inherently random, and is readily modeled by a stochastic differential equation. In this paper, we show that when the number of target molecules is much smaller than the number of probe molecules, the binding reaction can be described by the Cox-Ingersoll-Ross (CIR) process. Therefore, determining the number of target molecules requires finding parameters of a temporally sampled CIR process corrupted by noise. For this, we rely on a particle filter. Computational studies demonstrate effectiveness of the proposed scheme, and show that it outperforms competing techniques.