标题： 基于泊松点过程的随机泰勒展开 显示英文标题

标题： Stochastic Taylor expansion via Poisson point processes

摘要： 我们通过引入基于底层泊松点过程模型的随机公式，推广了泰勒定理。 我们利用这种方法提出了一种新的非线性回归框架，并对模型参数进行统计推断。 所提出的估计量的理论性质也被证明，包括其收敛性，以一致几乎必然的方式收敛到真实函数。 该理论适用于单变量和多变量情况，并通过模拟和对股票市场数据的应用，用几个例子说明了所提出的方法。 显示英文摘要

摘要： We generalize Taylor's theorem by introducing a stochastic formulation based on an underlying Poisson point process model. We utilize this approach to propose a novel non-linear regression framework and perform statistical inference of the model parameters. Theoretical properties of the proposed estimator are also proven, including its convergence, uniformly almost surely, to the true function. The theory is presented for the univariate and multivariate cases, and we exemplify the proposed methodology using several examples via simulations and an application to stock market data.