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Results tagged with pr.probability
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user 91273
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
-1
votes
What is an upper bound for $|E(X|\mathcal{A})-E(X)|$?
I guess $\alpha$-mixing condition might not be sufficient. Instead, we may need $\phi$-mixing conditions.
Without loss of generality, assume $1\ge X\ge 0$ almost surely.
Define $\phi$-mixing coeffi …
- 87
2
votes
What is the relationship between $E(X\mid\mathcal{A})$ and $E(X\mid A)$?
This is a simple question.
For any $A\in\mathcal{A}$, it holds that
$$
\int E(X\mid\mathcal{A})I_A \, dP=E(XI_A)=P(A)E(X\mid A)\le P(A),
$$
hence, $E(X\mid\mathcal{A})\le1$ almost surely..
Thanks …
- 87
4
votes
1
answer
1k
views
What is an upper bound for $|E(X|\mathcal{A})-E(X)|$?
Let $X$ be a random variable with $|X|\le1$, and $\mathcal{A}$ be a $\sigma$-algebra. What is an upper bound for $|E(X|\mathcal{A})-E(X)|$?
Existing results:
It has been known that $E|E(X|\mathcal{A …
- 87
0
votes
1
answer
193
views
What is the relationship between $E(X\mid\mathcal{A})$ and $E(X\mid A)$?
This question seems obvious, but not sure how to prove it.
Let $\mathcal{A}$ be a $\sigma$-algebra, and $X$ be a random variable.
Suppose $E(X\mid A)\le1$ for any $A\in\mathcal{A}$, can we conclude …
- 87