本文選題：g-期望　切入點(diǎn)：加權(quán)g-期望　出處：《中國(guó)礦業(yè)大學(xué)》2017年碩士論文

【摘要】：本文主要研究加權(quán)g-期望與倒向重隨機(jī)微分方程的若干問(wèn)題.第一章介紹了研究背景、研究現(xiàn)狀及主要研究?jī)?nèi)容,詳細(xì)介紹了g 期望的基本概念及相關(guān)性質(zhì),為后文的研究工作提供了理論基礎(chǔ).第二章主要在g-期望的基礎(chǔ)上給出了加權(quán)g-期望的概念,探索了加權(quán)g-期望的平移不變性、擬次可加性與關(guān)于λ的單調(diào)性.在此基礎(chǔ)上,進(jìn)一步研究得到基于加權(quán)g-期望的Jensen不等式,矩不等式以及大數(shù)定律,證明了當(dāng)生成元g關(guān)于y非增且關(guān)于(y,z)滿(mǎn)足正齊次性時(shí),基于加權(quán)g-期望的矩不等式一般成立;在λ ≥1/2且生成元g不依賴(lài)于y、關(guān)于z滿(mǎn)足超齊次性時(shí),建立了基于加權(quán)g-期望的Jensen不等式;當(dāng)g關(guān)于z滿(mǎn)足次線(xiàn)性時(shí),建立了基于加權(quán)g-期望的大數(shù)定律.第三章在經(jīng)典方差定義的基礎(chǔ)上,我們研究了加權(quán)g-方差與加權(quán)g-協(xié)方差的性質(zhì),加權(quán)g-方差、加權(quán)g-協(xié)方差與生成元之間的關(guān)系以及加權(quán)g-方差、g-方差與經(jīng)典方差之間的關(guān)系.第四章研究線(xiàn)性增長(zhǎng)條件下的倒向重隨機(jī)微分方程,在生成元f關(guān)于(y,z)連續(xù)且線(xiàn)性增長(zhǎng)、生成元g關(guān)于(y,z)滿(mǎn)足Mao的非Lipschitz條件下,得到了其最小解的存在定理。
[Abstract]:In this paper, some problems of weighted g-expectation and backward heavy stochastic differential equations are studied. In Chapter 1, the research background, research status and main research contents are introduced, and the basic concepts and related properties of g-expectation are introduced in detail. In the second chapter, we give the concept of weighted g-expectation on the basis of g-expectation, explore the translation invariance of weighted g-expectation, quasi-subadditivity and monotonicity about 位. The Jensen inequality, moment inequality and law of large numbers based on weighted g-expectation are obtained. It is proved that the moment inequality based on weighted g-expectation is generally true when the generator g satisfies the positive homogeneity. When 位 鈮，

本文編號(hào)：1679828