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学术报告

【北航数学论坛(9.9, Teturo Kamae)】 Deterministic Brownian motion
发布日期:2019-09-08  浏览量:

北航数学论坛

题目: Deterministic Brownian motion

报告人:Teturo Kamae教授(大阪市立大学)

报告时间:2019.9.9 10:00-11:00

报告地点:319学院路校区)

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 [1], which comes from a piecewise linear function called N-function .                                          

One of the motivations of the study is given by Benoit B. Mandelbrot [2], 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.  

[1] Teturo Kamae, Stochastic analysis based on deterministic Brow-

nian motion, Israel J. Math. 125 (2001) pp.317-346.

[2] Benoit B. Mandelbrot, A multifractal walk down Wall Street, Sci-

enti_c American, February 1999.

个人简介:

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。

邀请人:薛玉梅

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