Martingale criterion (discrete time)

Theorem.

Let $X=(X_{n},\\mathcal{F}_{n})$ be a local martingale. If there is an $n_{0}\\in\\mathbb{N}$ such that $\\forall\\ n\\geq n_{0},n\\in\\mathbb{N}$ either:

\\displaystyle EX_{n}^{-}

\\displaystyle<\\infty

or:

\\displaystyle EX_{n}^{+}

\\displaystyle<\\infty

Then $X$ is a martingale.

随便看

数学辞典收录了18232条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。