题目: Deterministic Brownian motion
摘要: Deterministic Brownian motions are stochastic processes with non-correlated, stationary and strictly ergodic increments having 0-entropy and 0-expectation. The self-similarity of order
follows from these properties. Among the deterministic Brownian motions, the simplest one is the N-process
defined and studied in , which comes from a piecewise linear function called N-function .
One of the motivations of the study is given by Benoit B. Mandelbrot , who mentioned that the simulation of stock market by the Brownian motion contains too much randomness. Actual market has a strong negative correlation between the fluctuations of price on a day and the next day. He is suggesting to use the N-shaped function as the base of the simulation.
Our model has a lot of similarities to the It^o process. For example, we have a kind of It^o formula. Nevertheless, there is a big difference between them. Our process has 0-entropy while It^o process has
-entropy. Therefore, we have much better possibility of predicting the future.
 Teturo Kamae, Stochastic analysis based on deterministic Brow-
nian motion, Israel J. Math. 125 (2001) pp.317-346.
 Benoit B. Mandelbrot, A multifractal walk down Wall Street, Sci-
enti_c American, February 1999.
Teturo Kamae教授现为Osaka City University特聘教授。曾担任过系主任，理学院院长，学术委员会主任，基金委主任，大阪数学期刊的主编等职务.他是概率统计、游戏理论、分形、组合理论、动力系统等领域内的很活跃的国际上著名的高水平专家，并在这些领域上作出了杰出的贡献。在各个领域的权威期刊上发表100余篇高水平的学术论文，有专著5本。同时经常被邀请在学术会议上作1小时的报告。并经常被聘请为法国、俄罗斯、美国、以色列、中国等著名大学的讲习教授。多次作为引智专家访问北航。