As a concrete setting where stochastic partial differential equations (SPDEs) are able to model real phenomena, we propose a stochastic Meinhardt model for cell repolarisation and study how parameter estimation techniques developed for simple linear SPDE models apply in this situation. We establish the existence of mild SPDE solutions and we investigate the impact of the driving noise process on pattern formation in the solution. We then pursue estimation of the diffusion term and show asymptotic normality for our estimator as the space resolution becomes finer. The finite sample performance is investigated for synthetic and real data.

翻译：作为能够模拟真实现象的随机局部偏差方程(SPDEs)的具体环境,我们提出一个用于细胞再极化的随机偏差Meinhardt模型,并研究在这种情况下如何应用为简单的线性SPDE模型开发的参数估计技术。我们确定是否存在温和的SPDE解决方案,并调查驱动噪音过程对解决方案模式形成的影响。我们接着对扩散术语进行估计,并在空间分辨率变得精细时显示我们的估计值的无症状正常度。对合成和真实数据的有限样本性能进行了调查。