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Just a layman and slow learner. Thank you for your enlightenment and patience, and for giving me the best memory in my life.


May
6
comment How to solve this PDE?
Thanks! Do you also know what page(s) on that book are relevant to solving my PDE?
May
6
revised How to solve this PDE?
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May
6
accepted Continuous a.s. process
May
6
comment Continuous a.s. process
(4) Does "2.No" mean you agree with that the three quoted definitions not having continuity a.s. are correct?
May
6
comment Continuous a.s. process
@Shai: Thanks! I was wondering: (1) what parts in the three definitions respectively imply continuity a.s.? (2) how "any constant function corresponds to a Gaussian process" can be a counterexample, isn't constant function continuous a.s.? (3) in Wikipedia en.wikipedia.org/wiki/…, the definition of Wiener process explicitly requires continuity a.s. besides those said in the first definition quoted in my post. So is it redundant in Wikipedia's definition?
May
6
asked Continuous a.s. process
May
5
asked Probability generating function, moment generating function and characteristic function
May
5
comment How to solve this PDE?
@Jonas: a is constant. (1) I am still having trouble to understand the method of characteristics. Would you mind explain some more? (2) Also can separation of variables apply here? (3) Usually, which method is chosen for which type of PDE? Thanks!
May
5
asked How to solve this PDE?
May
4
comment Elementary and measure definitions of conditional expectation and probability
@Didier: Thanks! My mistake. I have replaced Y in P(Y|X=x) and P(Y|X) with a measurable set A. How about now?
May
4
revised Elementary and measure definitions of conditional expectation and probability
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May
4
asked Elementary and measure definitions of conditional expectation and probability
May
4
comment Questions about independence between random variable and $\sigma$-algebra
Thanks! For 2, a random variable and a sigma algebra are independent, if the sigma algebra and the sigma algebra generated by the random variable are independent. Two sigma algebras are independent, if any two subsets, each from each sigma algebra, are independent. But I still can see how 2 can be derived from the definitions.
May
4
asked Questions about independence between random variable and $\sigma$-algebra
May
3
asked Dynamic programming problem and shortest path problem
May
3
comment Different versions of Riesz Theorems
@Theo: Thanks! You didn't misunderstand me.
May
3
comment Different versions of Riesz Theorems
@Theo: Thanks! On $L_2$ space as a Hilbert space with the usual inner product, will the three coincide?
May
3
comment Different versions of Riesz Theorems
@Theo: Thanks! In your first sentence, by "when $X$ is finite", do you mean 1 and the others coincide for $L_2(X)$?
May
3
revised Different versions of Riesz Theorems
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May
3
asked Different versions of Riesz Theorems