Randomness of the Gaussian variable and vectors

Zhixuan Dai; Liai Zhang

doi:10.1117/12.2628015

22 April 2022 Randomness of the Gaussian variable and vectors

Zhixuan Dai, Liai Zhang

Proceedings Volume 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021); 121632R (2022) https://doi.org/10.1117/12.2628015
Event: International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 2021, Nanjing, China

Abstract

Stochastic process is developing vigorously both in theory and application. Its basic knowledge and methods are not only necessary for mathematics and probability statistics majors, but also for applications and research in fields such as communication, control, biology, social science, engineering technology, and economy. For example, the splitting of atoms, the decay of radioactivity; the processing of audio and video signals, the ups and downs of the stock market; the growth of biological populations, and the spread of infectious diseases are all closely related to stochastic process. Stochastic process studies how random variables change with time parameters. In the study of stochastic process, people describe the internal laws of necessity through the appearance of contingency, and describe these laws in the form of probability to realize necessity from the contingency. Probability is a subject of uncertain phenomena, which reveals the manifestation of internal laws contained in accidental phenomena and plays an important role in people's understanding of natural and social phenomena. This paper mainly introduces the definition and theorem proof of Gaussian variable and Gaussian vector for the purpose of taking investigation of Brownian motion in the future.

Citation Download Citation

Zhixuan Dai and Liai Zhang "Randomness of the Gaussian variable and vectors", Proc. SPIE 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 121632R (22 April 2022); https://doi.org/10.1117/12.2628015

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KEYWORDS

Stochastic processes

Probability theory

Mathematical modeling

Vector spaces

Network security

Statistical analysis

Chemical species

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