广义Mandelbrot乘积瀑布与上临界迁出分枝过程的鞅收敛速率

发布时间：2018-08-22 10:38

【摘要】：本文主要研究了广义Mandelbrot乘积瀑布的中心极限定理及上临界迁出分枝过程的鞅收敛速率,全文共分为三章:第一章绪论.本章介绍了广义Mandelbrot乘积瀑布模型以及上临界迁出分枝过程的研究背景和发展现状,然后分别介绍了广义Mandelbrot乘积瀑布与上临界迁出分枝过程的具体模型、研究思路及主要结果.第二章广义Mandelbrot乘积瀑布.本章着重研究广义乘积瀑布模型中心极限定理.首先验证了Y_n是一个非负鞅,给出了Y_n-Y_∞的期望及方差的表达式及Y_∞的方差性质,然后应用Lindeberg-Feller中心极限定理,明了广义Mandelbrot乘积瀑布的中心极限定理.第三章上临界迁出分枝过程.本章着重研究上临界迁出分枝过程,给出了该过程的一些基本性质,如过程的期望及方差,并考虑了规范化过程的收敛问题.
[Abstract]:In this paper, we mainly study the central limit theorem of generalized Mandelbrot product waterfall and the convergence rate of martingale in the upper critical migration out of branch process. The whole paper is divided into three chapters: chapter one is an introduction. This chapter introduces the research background and development status of generalized Mandelbrot product waterfall model and the upper critical migration out branching process, and then introduces the specific models of generalized Mandelbrot product waterfall and upper critical migration branch process, the research ideas and main results. Chapter 2 Generalized Mandelbrot Product Falls. This chapter focuses on the central limit theorem of generalized product waterfall model. First, it is proved that Yn is a nonnegative martingale. The expressions of the expectation and variance and the variance property of Y _ 鈭，

本文编号：2196845