Ito Process 的条件期望是 Martingale 吗？

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在准备考试，很早以前学的却想不起来是不是对的
If X_t is an Ito process, then its conditional expectations Y_t = E_t[X_t] is a Martingale.
这句话是不是对的？

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关键词：Martingale Process Martin artin Mart process

obviously incorrect.

1.one can only say a process is a martingale, not the conditional one. pls check the definition of conditional expectation.

2. unfortunately, ito process isnot a martingale, generally. ito process=martingale+bounded variation due to Doob-Meyer decompostion (you could browerse your book), where the latter part make it unnecessary to be a martingale.

当然是Martingale

E(E(X|F(t+n))|F(t))=E(X|F(t))，条件期望的期望等于无条件期望。

楼上不知道别乱说

关于R.Var.的条件期望一定是鞅

hilbertan 发表于 2011-12-21 18:41
当然是Martingale

E(E(X|F(t+n))|F(t))=E(X|F(t))，条件期望的期望等于无条件期望。

Sorry, your meaning is correct. I misunderstood the content.

can I ask what exam that u were preparing for ?
cuz I have same question, but we do not have textbook to refer to .. ..

please refer to Levy martingale

I think any adapted process has this property. Correct me if I am wrong.

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