Equivalence Between Representations for Samplable Stochastic Processes and its Relationship With Riesz Bases

Medina; J.M.; Cernuschi-Frias; B.

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Equivalence Between Representations for Samplable Stochastic Processes and its Relationship With Riesz Bases

机译：可简化随机过程表示之间的等价关系及其与Riesz基的关系

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摘要

We characterize random signals which can be linearly determined by their samples. This problem is related to the question of the representation of random variables by means of a countable Riesz basis. We study different representations for processes which are linearly determined by a countable Riesz basis. This concerns the representation of continuous time processes by means of discrete samples.

机译：我们表征可以由其样本线性确定的随机信号。这个问题与借助于可数的Riesz基表示随机变量的问题有关。我们研究由可数Riesz基础线性确定的过程的不同表示形式。这涉及通过离散样本表示连续时间过程。

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来源
《IEEE Transactions on Information Theory》 |2013年第10期|6932-6938|共7页
作者
Medina; J.M.; Cernuschi-Frias; B.;
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作者单位

Dpto. Matemática, Facultad de Ingeniería, Universidad de Buenos Aires and Instituto Argentino de Matemática – CONICET Argentina, República Argentina|c|;

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原文格式 PDF
正文语种 eng
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关键词
Finite variance random processes; KL-expansions; Riesz bases; reproducing kernel Hilbert space; sampling;

机译：有限方差随机过程;KL展开;Riesz基;再现核希尔伯特空间;采样;

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专利

1. A generalization of inverse distance weighting and an equivalence relationship to noise-free Gaussian process interpolation via Riesz representation theorem [J] . De Mulder Wim, Molenberghs Geert, Verbeke Geert Linear & Multilinear Algebra: An International Journal Publishing Articles, Reviews and Problems . 2018,第5a8期

机译：逆距离加权的概括和通过RIESZ表示定理的无噪声高斯过程插值的等价关系
2. Evaluation of Karhunen-Loeve, spectral, and sampling representations for Stochastic processes [J] . Grigoriu M Journal of Engineering Mechanics . 2006,第2期

机译：评估随机过程的Karhunen-Loeve，频谱和采样表示
3. Random function based spectral representation of stationary and non-stationary stochastic processes [J] . Liu Zhangjun, Liu Wei, Peng Yongbo Probabilistic engineering mechanics . 2016,第jula期

机译：基于随机函数的平稳和非平稳随机过程的频谱表示
4. STOCHASTIC EQUIVALENCE OF CPDP-AUTOMATA AND PIECEWISE DETERMINISTIC MARKOV PROCESSES [C] . Stefan Strubbe, Arjan van der Schaft IFAC (International Federation of Automatic Control) World Congress . 2005

机译：CPDP-自动和分段确定性马尔可夫过程的随机等价
5. Information Flow in Stochastic Optimal Control and a Stochastic Representation Theorem for Meyer-Measurable Processes =Informationsfluss in der stochastisch optimalen Steuerung und ein Darstellungstheorem für Meyer-messbare Prozesse [D] . Besslich, David. 2019

机译：随机最佳控制中的信息流程和Meyer可测量过程的随机表示定理=用于迈尔可测量过程的随机最佳控制中的信息流程和表示定理
6. REPRESENTATION OF A CLASS OF STOCHASTIC Processes [O] . Samuel Karlin, James McGregor 1955

机译：一类随机过程的表示
7. IDENTIFYING CAUSAL RELATIONSHIPS BETWEEN NONSTATIONARY STOCHASTIC PROCESSES: AN EXAMINATION OF ALTERNATIVE APPROACHES IN SMALL SAMPLES [O] . Zapata Hector O., Hudson Michael A., Garcia Philip 100

机译：识别非平稳随机过程之间的因果关系：对小样本中替代方法的检验
8. Stochastic Integral Representation of Stable Processes with Sample Paths in Banach Spaces [R] . Rosinski, J. 1985

机译：Banach空间中具有样本路径的稳定过程的随机积分表示

Equivalence Between Representations for Samplable Stochastic Processes and its Relationship With Riesz Bases

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