DonskerVaradhan Type Large Deviation Principles for Ustatistics
Project/Area Number  10640113 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  Kanazawa University 
Principal Investigator 
NAKAGAWA Shuya Kanazawa University, Faculty of Engineering, Professor, 工学部, 教授 (50185899)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥3,200,000 (Direct Cost : ¥3,200,000)
Fiscal Year 1999 : ¥1,100,000 (Direct Cost : ¥1,100,000)
Fiscal Year 1998 : ¥2,100,000 (Direct Cost : ¥2,100,000)

Keywords  large deviation / Ustatistics / Vstatistics / stochastic differential equation / EulerMaruyama scheme / Brownina motion / Large Deviation / Stochastic Differeutial Equation / Stochartic Differeutial Eguqtion / U統計量 / 大域偏差理論 / ノンパラメトリック統計 
Research Abstract 
The investigator investigated large deviation principles for symmetric statistics using new technique which is an application of limit theorems for Banach space valued i.i.d. random variables. Usually well known Hoeffding decomposition for symmetric scholastics cannot be used for symmetric statistics with nondegenerate kernels. He solved by the method to obtain DonskerVaradhan type large deviation principles. The numerical solution of Ito's stochastic differential equation (SDE) is realized by pseudorandom numbers which are defined by some algebraic algorithms in terms of an approximate solution on computers. Since any algorithm has an essential defect for independence and distribution, as Knuth (1981) pointed out. The investigator focused on the distribution of pseudorandom numbers and consider the error estimation of the EulerMaruyama approximation when the distribution of underlying random variables is different from the normal distribution. One of important problems in stochastic analysis is to consider stochastic differential equations with boudary conditions on multidimensional domains (socalled Skorohod SDE). There are two approaches to define approximate solutions of such stochastic differential equations. Saisho (1987) constructed Skorohod equations using the projection on the boundary. Roughly speaking, the reflecting path is defined for given function by the following manner : Define a step function by discretization of the Brownian motion and construct the reflecting step function for the Brownian motion. The investigator define EulerMaruyama type approximate solutions of it using penalty method and investigate the rate of convergence.

Report
(4results)
Research Output
(13results)