The law of small numbers and limit theorems of symmetric statistics

Access this Article

博士論文

Table of contents / p3 (0004.jp2)
Chapter1.Introduction / p1 (0006.jp2)
1.1.An overview of limit theorems of symmetric statistics / p3 (0008.jp2)
1.2.Results / p11 (0016.jp2)
1.3.Preliminaries / p15 (0020.jp2)
Chapter2.Multiple Poisson-Wiener-Ito integrals / p24 (0029.jp2)
2.1.Definition of a norm ∥･∥ / p25 (0030.jp2)
2.2.Properties of multiple Poisson-Wiener-Ito integrals / p33 (0038.jp2)
2.3.Convergence of multiple Poisson-Wiener-Ito integrals / p41 (0046.jp2)
Chapter3.Limit theorems for independent arrays / p45 (0050.jp2)
3.1.The law of small numbers for independent arrays / p46 (0051.jp2)
3.2.Asymptotic distributions of symmetric statistics when random elements have different distributions / p51 (0056.jp2)
3.3.Remarks for the identically distributed case / p57 (0062.jp2)
Chapter4.Limit theorems with the mixing condition / p69 (0074.jp2)
4.1.A Mixing condition / p69 (0074.jp2)
4.2.The law of small numbers with the mixing condition / p71 (0076.jp2)
4.3.Asymptotic distributions of symmetric statistics with the mixing condition / p80 (0085.jp2)
Chapter5.Examples / p84 (0089.jp2)
5.1.Symmetric polynomials / p84 (0089.jp2)
5.2.Non-interacting particle systems / p88 (0093.jp2)
Chapter6.Discussions / p91 (0096.jp2)
6.A.Distributions of some statistics constructed by the heteroscedastic method / p91 (0096.jp2)
6.B.Limit theorems for stochastic processes / p101 (0106.jp2)
References / p107 (0112.jp2)