无论是宇宙的起源、生物的进化，还是股市的涨跌、天气的变化，都伴随着不确定性。人类在探索世界的过程中，越来越深刻地意识到不确定性因素无时无刻不在发挥着重要作用。随机过程就是对这些不确定性因素进行描述的一种数学方法。

源于对物理现象的研究，包括玻尔兹曼、爱因斯坦在内的许多物理学家对随机过程理论的发展发挥了巨大的推动作用。苏联数学家 柯尔莫哥洛夫 （Andrey Nikolayevich Kolmogorov）和美国数学家 杜布 （Joseph Leo Doob）的杰出贡献最终奠定了随机过程的理论基础。现在，随机过程已经广泛应用于物理、化学、生物、信息、计算机等诸多领域。而由于金融市场内在的不确定性，随机过程很自然地渗透进了金融领域，尤其在衍生品的估价和风险管理方面业已成为一种应用广泛的建模方法。

Biography: Joseph Leo Doob（1910—2004）, a pioneer in the study of the mathematical foundations of probability theory and its remarkable interplay with other areas of mathematics. In 1940, he began a systematic development of martingale theory, the focus of one of the chapters, nearly 100 pages long, in his 1953 book "Stochastic Processes." This treatise of over 650 pages has been one of the most important and influential books on probability since Laplace's 1812 book.（Sources: https://math.illinois.edu/resources/department-history/faculty-memoriam/joseph-doob）

Biography: Andrey Nikolayevich Kolmogorov, (born April 25 [April 12, Old Style], 1903, Tambov, Russia—died Oct. 20, 1987, Moscow), Russian mathematician whose work influenced many branches of modern mathematics, especially harmonic analysis,probability, set theory, information theory, and number theory. A man of broad culture, with interests in technology, history, and education, he played an active role in the reform of education in the Soviet Union. He is best remembered for a brilliant series of papers on the theory of probability. (Sources: https://www.britannica.com/biography/Andrey-Nikolayevich-Kolmogorov)

Core Functions and Syntaxes

本章核心命令代码

ax.scatter3D（）绘制三维立体散点图

DataFrame.pct_change（）计算变化率

isoweekday（）返回一星期中的每几点，星期一为1

matplotlib.pyplot.axes（projection='3d'）定义一个三维坐标轴

numpy.concatenate（）将多个数组进行连接

numpy.cumsum（）产生沿某一轴的数据元素的相加累积值

numpy.random.choice（）从一组数据中随机选取元素，并将选取结果放入数组中返回

pandas.date_range（）指定日期范围

pandas.Timedelta（）设定时间增量

pandas.to_datetime（date, format="%Y-%m-%d"）依照设定格式转换产生日期格式数据

to_series（）创建一个索引和值都等于索引键的序列 8ypZKGJS8OmZNAh7KJSfpu5zCyW+D9qxy2idn1q/vJIci6jvDsX/nUz8DhlZMBza