Doob wrote a book of over 800 pages: Classical Potential Theory and Its Probabilistic Counterpart.The first half of this book deals with classical potential theory and the second half with probability theory, especially martingale theory. In writing this book, Doob ...
Temme. A trajectorial interpretation of doob's martingale inequalities. Ann. Appl. Prob, 23(4):1494-1505, 2013.ABP+12] B. Acciaio, M. Beiglbo¨ck, F. Penkner, W. Schachermayer, and J. Temme. A trajectorial interpretation of Doob's martingale inequalities. Ann. Appl. Probab., 2012....
接下来我们证明Doob Meyer分解定理,将鞅和下鞅的关系联系起来: 如果X 是一个下鞅,那么存在唯一的适应的随机过程(M,k),使得:1) X_t = M_t - k_t,\forall t \\ 2) M \text{ is a martingale process} \\ 3) k_0 = 0, k \text{ is an increasing and predictable process, which means } ...
In this paper we deal with the martingales in variable Lebesgue space over a probability space. We first prove several basic inequalities for conditional expectation operators and give several norm convergence conditions for martingales in variable Lebesgue space. The main aim of this paper is to inv...
J. Lai, The Bellman functions of the Carleson Embedding Theorem and the Doob's martingale in- equality, arXiv:1411.5408 [math.CA], 2014, 18 pp.Jingguo Lai, The Bellman functions of the Carleson Embedding Theorem and the Doob's martingale inequality, arXiv:1411.5408v2....
Doob’s Optional Stopping Theorem:If the sequence S(0),S(1),S(2),...is a bounded martingale,and T is a stopping time, then the expected value of S(T)is S(0).Most real world asset prices are not martingales,even in theory.So why is this theorem relevant tofinance?1.Many asset...
鞅(Martingale) 概率论 随机过程 赞同303 条评论 分享喜欢收藏申请转载 写下你的评论... 3 条评论 默认 最新 数学小萌新 Lp极大不等式证明的 第二个等号为啥成立 2022-10-20· 上海 回复喜欢 flyingczx 作者 感谢关注,这里是我写错了。这里应是小于等于号,用的是D...
A trajectorial interpretation of Doob's martingale inequalitiesA stopped Doob inequality for stochastic convolution integrals and stochastic evolution equationsThe Irreducible Modules of the Terwilliger Algebras of Doob SchemesOptimal Stopping and Best Constants for Doob-like Inequalities I: The Case $p = ...
Doob不等式和Doob分解定理的理解(未完) 鞅论里面重要内容还不甚清晰的是Doob 不等式和Doob分解定理。 Doob不等式 根据我的理解,可以来证明鞅的收敛。 Doob不等式的证明非常基本,只用到了|X|是凸函数那么是一个submartingale。 lp形式用到了分部积分,Fubini定理和holder 不等式。
Kikuchi, M.: On some martingale inequalities for mean oscillations in weak spaces. Ric. Mat. doi:10.1007/s11587-015-0224-1 Kreĭn, S.G., Petunin, Yu.I., Semenov, E.M.: Interpolation of linear operators. Translations of Mathematical Monographs, vol. 54. American Mathematical Society, ...