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Fractal and Stochastic Process

分形和随机过程

基本信息

批准号：
09440086
负责人：
KAMAE Teturo
金额：
$ 4.74万
依托单位：
Osaka City University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B).
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 2000
项目状态：
已结题

项目摘要

In this research, we studied among all a deterministic version of the Ito calculus.Deterministic Brownian motions are stochastic processes with noncorrelated, stationary and strictly ergodic increments having 0-entropy and 0-expectation. The self-similarity of order 1/2 follows from these properties. Such processes have a lot of variety and have different properties. It is not the case of the Brownian motion where the process is characterized as a process with stationary and independent increments with 0-expectation and standard variance.Among the deterministic Brownian motions, the simplest one is the N-process (N_t ; t∈R). We consider a process Y_t=H (N_t, t), where the function H(x, s) is twice continuously differentible in x and once continuously differentible in s and H_x(x, s)>0. The function H is consisered completely unknown except for these properties. We want to predict the value Y^c from the observation Y_J : ={Y_t ; t∈J}, where J=[a, b] and a<b< c. We proved that there exists a estimator Y_c such that<<numerical formula>>as c↓b with the following C (b) as the constant in O ( ) :<<numerical formula>>

在这项研究中，我们研究了所有的确定性版本的伊藤演算。确定性布朗运动是随机过程的不相关，平稳和严格遍历增量具有0-熵和0-期望。1/2阶的自相似性来自这些性质。这样的过程有很多种类，并且具有不同的性质。在确定性布朗运动中，最简单的是N-过程（N_t ; t∈R）。考虑过程Y_t=H（N_t，t），其中函数H（x，s）在x中二次连续可微，在s中一次连续可微，且H_x（x，s）>0.除了这些性质之外，函数H是完全未知的。我们希望从观测值Y_J：={Y_t ; t∈J}预测值Y^c，其中J=[a，B]且a<B< c。我们证明了存在一个估计量Y_c使得<<numerical formula>>作为c↓B，其中C（B）是O（）中的常数：<<numerical formula>>