Randomness of the Gaussian variable and vectors
Zhixuan Dai, Liai Zhang · International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021) · 2022
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.