This paper is devoted to the conditional density estimation for continuous time processes with values in functional spaces. Under standard assumptions, we prove the uniform convergence of the conditional density estimator, from which we deduce the almost sure convergence of the conditional mode estimator. Then, the convergence of the conditional distribution function and the regression function estimators are established.

中文翻译：

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函数空间中具有值的连续时间过程的条件密度估计

本文致力于在函数空间中具有值的连续时间过程的条件密度估计。在标准假设下，我们证明了条件密度估计量的一致收敛性，由此推导出条件模式估计量几乎肯定收敛。然后，建立条件分布函数和回归函数估计量的收敛性。