Stochastic analysis based on deterministic Brownian motion

被引：4

作者：

Kamae, T ^{[1
]}

机构：

[1] Osaka City Univ, Dept Math, Osaka 5588585, Japan

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2001年 / 125卷 / 1期

关键词：

BROWNIAN Motion; Sample Path; Stochastic Analysis; Deterministic Version; Countable Dense Subset;

D O I：

10.1007/BF02773385

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A deterministic version of the Ito calculus is presented. We consider a model Y-t = H (N-t, t) with a deterministic Brownian N-t and an unknown function H. We predict Y-c from the observation {Y-t;t is an element of [a,b]}, where a < b < c. We prove that there exists an estimator Yt based on the observation such that E[((Y) over cap (t) - Y-c)(2)] = O((c - b)(2)) as c down arrow b.

引用

页码：317 / 346

页数：30