布朗運動及其應(yīng)用-wenkub
2023-07-13 09:41:11 本頁面
【正文】 l based on probability space, is considered the dynamics of probability theory, namely, it is the study of the random phenomena with time evolution. So the random behavior is a kind of statistical rules of behavior. The price behavior models are usually expressed in the famous Wiener process. We assume that the Wiener process the stock price following the general is tempting, that is to say, it has the expected drift rate and variance rate. The Wiener process indicates that only the values of variables associated with future projections, past history variables and variables from the past to the present and the future evolution of the way the stock price forecast is not relevant. The Maldives Kopf and the nature of the weak market efficiency (the weak form of market efficiency) is consistent, that is to say, a stock price already contains all the information, including all the past records of prices. But when people began to study the financial market by using fractal theory, found its operation does not follow the Brown campaign but to more general fractional Brown motion.Brown movement throughout the financial field, in the modern financial field occupies an important position.Brown refers to a random walk without correlation, meet the statistical self similarity characteristics with random fractal, but the function of time (trajectories) self affine function is available. Said: (as) (0) Xtt is the standard Brown motion, then each of the following is the standard Brown random function 1, (21).) (/) from XtcXtc (c 0 is a constant, t = 0), 2 (2)) () (XtXthhX) (H 0 is a constant, t = 0), 13 (3)) (0) (0) (0) tXttXttThe motion of particles is very much in the form of translation and its transfer. It is obvious that the particles are not related to each other. Even when the particles are close to each other, the particle motion is not affected by the particle size.Bach Leigh Ye in France in 1900, the speculation theory, the stock price is also seen as a random movement, the resulting equation is very similar to the description of the Brown particle motion, but the resulting stock price may be negative, apparently inconsistent with the actual, Bach Leigh Ye socalled Brown movement, in other words, he put the stock price changes, the ideal for the Brown movement before the study, it represents the meaning of no rules, as long as the economy The research of control theory. Absorbed by founder Weiner in 1923 on the Brown campaign made a strict mathematical definition, according to this definition, the Brown movement is a kind of independent increment process, so it is a Markov process, the mathematical munity is often the Brown campaign called (1952): the the
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