Regularization effects of time integration on Gaussian process functionals

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications Pub Date : 2025-08-06 DOI:10.1016/j.spa.2025.104761

Takafumi Amaba , Marie Kratz

引用次数: 0

Abstract

In this paper, we investigate the regularization effects, in the sense of Malliavin calculus, on functionals of Gaussian processes induced by time integration, focusing on their covariance functions. We study several examples of important covariance functions classes to verify whether they satisfy the sufficient conditions proposed for regularization. Additionally, we derive a weak implication for the smoothness of level-crossing functionals.

查看原文本刊更多论文

时间积分对高斯过程泛函的正则化效应

本文研究了时间积分对高斯过程泛函的正则化效应，重点研究了它们的协方差函数。我们研究了几个重要的协方差函数类的例子，以验证它们是否满足正则化的充分条件。此外，我们还得到了平交道口泛函平滑性的一个弱暗示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Stochastic Processes and their Applications 数学-统计学与概率论

CiteScore

2.90

自引率

7.10%

发文量

180

审稿时长

23.6 weeks

期刊介绍： Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests. Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.