The chemical sensing process can be understood as the physical process consisting of binding and unbinding reactions on the sensing surface. The random nature of the reactions lead to fluctuations in the response of a sensor. The response of the sensor is modeled in the form of a stochastic differential equation (SDE). The model is developed by formulating the binding and unbinding reactions in the form of Bernoulli trials. The transition probability density function (pdf) of the number of binded analyte molecules $X_t$ , at a given time instant $t$ , has been evaluated using the Bernoulli trial representation. The obtained pdf is used to derive the Fokker Planck equation (FPE) for the stochastic process. The FPE has a direct correspondence with the desired SDE model. A maximum aposteriori (MAP) estimation method has been proposed for evaluating the parameters. The SDE model for the fluctuations in the sensor signal has been evaluated. The frequency spectrum of the fluctuations is evaluated using the SDE. The proposed model is used to analyze noise due to the ligand-receptor kinetics in the receiver in molecular communication. The utility of the model in agent identification applications has been demonstrated.

中文翻译：

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表征化学传感波动的随机模型

化学感测过程可以理解为由感测表面上的结合和未结合反应组成的物理过程。反应的随机性导致传感器响应的波动。传感器的响应以随机微分方程（SDE）的形式建模。通过制定伯努利试验形式的结合和非结合反应来开发模型。结合的分析物分子数量的跃迁概率密度函数（pdf）$ X_t $ ，在给定的时间瞬间 $ t $ ，已使用伯努利试验表示法进行了评估。获得的pdf用于导出随机过程的Fokker Planck方程（FPE）。FPE与所需的SDE模型具有直接对应关系。已经提出了最大撇号（MAP）估计方法来评估参数。已经评估了传感器信号波动的SDE模型。使用SDE评估波动的频谱。所提出的模型用于分析由于分子通讯中的受体中的配体-受体动力学而引起的噪声。已经证明了该模型在代理识别应用中的效用。