2009 Fiscal Year Final Research Report

Statistical asymptotic theory for stochastic processes And its computer implementation

Research Project

Project/Area Number	18500219
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	Statistical science
Research Institution	Kobe University (2007-2009) Hiroshima International University (2006)
Principal Investigator	SAKAMOTO Yuji Kobe University, 人間発達環境学研究科, 准教授 (70215664)
Project Period (FY)	2006 – 2009
Keywords	統計的推測 / 時系列解析 / モデル選択 / 数理ファイナンス
Research Abstract	The higher-order asymptotic expansions of many test statistics for stochastic processes are obtained, which leads to asymptotic expansion formulas of test statistics for diffusion processes. Highly accurate approximation formulas for major discriminant functions are derived in case of small or ergodic diffusion observations. Moreover, asymptotic expansions of marked point processes with time in-homogenous intensity functions are obtained, and using the mathematical formula manipulation, explicit expression of the coefficients in the expansions are given. Computer program for the approximation formulas obtained are coded, and their accuracy is measured numerically.

(2 results)