Dissertation > Excellent graduate degree dissertation topics show

Almost Surely Central Limit Theorem on the Maximum of Gaussian Vector Sequence

Author: ChenZhiCheng
Tutor: PengZuoXiang
School: Southwestern University
Course: Probability Theory and Mathematical Statistics
Keywords: Gaussian vector sequence extreme distribution almost surely central limit theorem local central limit theorem
CLC: O211.4
Type: Master's thesis
Year: 2007
Downloads: 37
Quote: 0
Read: Download Dissertation


This thesis is composed of almost surely central limit theorem on the maxima of weak dependent nonstationary Gaussian vector sequence under some conditions, and the almost surely local central limit theorems of the maximum of independent and identically distributed random variables. The main results are:Theorem A Suppsc X1,X2,…be standardized nonstationary Gaussian d dimensional random vectors satisfying (2.1) and (2.2). Let be constants such that, and let Uni(P),P = 1,…,d such thatλn(p)≥c(logn)1/2 for some c>0.ThenTheorem B Suppse X1, X2,…be standardized nonstationary Gaussian d dimensional random vectors satisfying (2.1), (2.2) and (2.3). Letλn(p)= Uni(p) be constants such that n(1 -Φ(λn(p))) is bounded. ThenTheorem C Suppse X1, X2,…be standardized nonstationary Gaussian d dimensional random vectors satisfying (2.1) and (2.2). Letλn(p) be constants such that n(1 -Φ(λn(p)))→τp as n→∞for someτ-≥O. ThenThorem D Suppse X1,X2,…be standardized nonstationary Gaussian d dimensionalrandomveetorswithδ= ma 1, and (2.5),(2.9) hold for some n→∞for someτp≥0, p = 1,…, d, thenTheorem E Suppse X1, X2,.. be d dimensional Gaussian random vectors with Yn = Xn+mn where satisfy Theorem 2.1.1 and mn, satisfy (2.6) and (2.7) respectively. Ifλn(p)≥c(logn)1/2 for some c>0, then whereTheorem F Suppse X1, X2,…be d dimensions random variables with Yn = Xn + mn where satisfy Theorem 2. 1. 2 and mn和satisfy (2. 6) and (2. 7) respectively. If (2. 8) holds for some D>0, then Theorem G Suppse X1, X2,…be standardized d dimensional nonstationary Gaussian random vectors withδ=1, and (2.5),(2.9) hold for some as for some O≤τpp<∞, thenTheorem H Let X1, X2,…be independent identically distributed random variables with EXi = 0, i = 1,2,….{un}, {un}. If F(un) - F(un)>andn(1 - F(un)) is bounded as Un<bn<un, thcnwhere

Related Dissertations

  1. Extremes of Mixed Distributions and Almost Sure Convergence Theorem of Maxima of Multivariate Gaussian Sequence,O211.4
  2. Almost Sure Convergence for Sample Range and Joint Asymptotic Distributions of Exceedances Point Process and Partial Sum,O211.4
  3. Limit Theorems on Gaussian Vector Sequences,O211.4
  4. The Statistical Analysis of Zero-Failure Data,O212
  5. Trends in Frequency and Intensity of Extreme Precipitation at Four German Stations in Recent 100 Years and Distribution Fit by Extreme Value Theory,P468.024
  6. Multivariate Compound Extreme Value Distribution Theory and Its Engineering Applications,P732.4
  7. Parameter Estimation of Lifetime Data in Weibull Distribution,O213
  8. Convergence and Stability of Numerical Solution of Stochastic Differential Equations with Piecewise Continuous Arguments,O211.63
  9. American Option Pricing under Stochastic Market Option Model Based on Dividend and Treatment Fees,O211.6
  10. The Study of Discrete Copula and Quasi-Copular,O211.6
  11. Copula-EGARCH-Kernel Density Estimation Model and Its Application,O211.3
  12. On the Risk Model Involving Two Classes of Claims with Threshold Dividend Strategy,O211.67
  13. Exponential distribution made ??up several Censored Accelerated test of quadratic estimates,O211.3
  14. Mixed Exponential Distribution under Censored Accelerated test of quadratic estimates,O211.3
  15. Some losses renewal equation equivalent conditions for asymptotic,O211.67
  16. Wide dependency structure and tail probability random Asymptotics,O211.5
  17. Increments with generalized negative dependency and the asymptotic behavior of random,O211.5
  18. The Model of Control and Model Calculations,O211.3
  19. Heterogeneity in Dynamic Discrete Choice Models,O211.62
  20. The Existence of Global Solution for Stochastic Functional Differential Equation,O211.63
  21. Dynamics Behavior of a Stochastic Delayed SIRS Model with Saturation Incidence,O211.6

CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Theory of probability ( probability theory, probability theory ) > Limit theory
© 2012 www.DissertationTopic.Net  Mobile