论文标题
在不同的措施和集成下，期望功能的Epi连接
Epi-Convergence of Expectation Functions under Varying Measures and Integrands
论文作者
论文摘要
对于指标空间的期望功能，我们为在不同的概率度量和集成量下提供了足够的条件，可以为筛子估计量，软体动物平滑，PDE限制的优化以及与期望约束的随机优化的应用中的应用。作为独立兴趣的表面连接的垫脚石，我们在轻度的可整合性假设下开发了参数fatou的引理。在SUSLIN度量空间的环境中，假设以Pasch-Hausdorff信封表示。对于一般度量空间，假设也转移到样品空间上集成的半接壤性，然后假定这是一个度量空间。
For expectation functions on metric spaces, we provide sufficient conditions for epi-convergence under varying probability measures and integrands, and examine applications in the area of sieve estimators, mollifier smoothing, PDE-constrained optimization, and stochastic optimization with expectation constraints. As a stepping stone to epi-convergence of independent interest, we develop parametric Fatou's lemmas under mild integrability assumptions. In the setting of Suslin metric spaces, the assumptions are expressed in terms of Pasch-Hausdorff envelopes. For general metric spaces, the assumptions shift to semicontinuity of integrands also on the sample space, which then is assumed to be a metric space.
