We consider a stochastic individual-based model in continuous time to describe a size-structured population for cell divisions. This model is motivated by the detection of cellular aging in biology. We here address the problem of nonparametric estimation of the kernel ruling the divisions based on the eigenvalue problem related to the asymptotic behavior in large population. This inverse problem involves a multiplicative deconvolution operator. Using Fourier techniques we derive a nonparametric estimator whose consistency is studied. The main difficulty comes from the nonstandard equations connecting the Fourier transforms of the kernel and the parameters of the model. A numerical study is carried out and we pay special attention to the derivation of bandwidths by using resampling.

中文翻译：

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基于偏微分方程平稳分布近似的碎片核的非参数估计

我们在连续时间内考虑基于个体的随机模型来描述细胞分裂的大小结构群体。该模型的动机是检测生物学中的细胞老化。我们在这里解决了基于与大种群中的渐近行为相关的特征值问题的划分的核的非参数估计问题。这个逆问题涉及乘法反卷积算子。使用傅立叶技术，我们推导出了一个非参数估计量，其一致性得到了研究。主要困难来自连接核的傅里叶变换和模型参数的非标准方程。进行了数值研究，我们特别注意使用重采样来推导带宽。