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 theBrownian motion contains too much randomness. Actual market hasa strong negative correlation between the fluctuations of price on aday and the next day. He is suggesting to use the N-shaped functionas 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 differencebetween them. Our process has 0-entropy while It^o process has
-entropy. Therefore, we have much better possibility of predicting thefuture.
 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。