【摘要】：本文主要研究了廣義Mandelbrot乘積瀑布的中心極限定理及上臨界遷出分枝過程的鞅收斂速率,全文共分為三章:第一章緒論.本章介紹了廣義Mandelbrot乘積瀑布模型以及上臨界遷出分枝過程的研究背景和發(fā)展現(xiàn)狀,然后分別介紹了廣義Mandelbrot乘積瀑布與上臨界遷出分枝過程的具體模型、研究思路及主要結(jié)果.第二章廣義Mandelbrot乘積瀑布.本章著重研究廣義乘積瀑布模型中心極限定理.首先驗(yàn)證了Y_n是一個非負(fù)鞅,給出了Y_n-Y_∞的期望及方差的表達(dá)式及Y_∞的方差性質(zhì),然后應(yīng)用Lindeberg-Feller中心極限定理,明了廣義Mandelbrot乘積瀑布的中心極限定理.第三章上臨界遷出分枝過程.本章著重研究上臨界遷出分枝過程,給出了該過程的一些基本性質(zhì),如過程的期望及方差,并考慮了規(guī)范化過程的收斂問題.
[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，

本文編號：2196845