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Apr
10
accepted About the notation in probability theory
Apr
2
comment Random variables with random indexes
thanks Liu Gang, it was helpful, what you suggest seems like true. Then I will try to derive the case that $I_n$ is a Markov process.
Apr
2
asked Random variables with random indexes
Mar
6
comment About the notation in probability theory
Thanks Did! I am more or less aware of this notation but what I couldn't make sense is for instance what is the meaning of $P(\{\omega\in\Omega\mid \exists n\geqslant1,X_n(\omega)=0\})$ precisely? There exists $n\geq 1$ s.t. $X_n = 0$ with probability one? How this implies that the walk will come to the position $X_n = 0$ infinitely often?
Mar
5
revised About the notation in probability theory
added 131 characters in body
Mar
5
asked About the notation in probability theory
Feb
19
accepted Convergence of a stochastic process to another?
Feb
19
comment Convergence of a stochastic process to another?
thanks! I did not think about this.
Feb
19
asked Convergence of a stochastic process to another?
Nov
17
asked A question related to independence and expectation
Nov
13
revised Show that the following are monotone classes
added 15 characters in body
Nov
13
accepted If $\{f_j\}$ is a sequence of measurable functions, then $\sup_j f_j(x)$ is measurable.
Nov
13
asked Show that the following are monotone classes
Nov
13
comment What is this set?
Hello, thanks for the intuition. I also wonder about what is the above set precisely? Can you decode that?
Nov
13
comment $2(1+abc)+\sqrt2(1+a^2)(1+b^2)(1+c^2)\ge(1+a)(1+b)(1+c)$ for real numbers $a,b,c$
Note to the translator: The translation is true.
Nov
12
comment Independence in infinite sequence of random variables
@n.c. I am a sort of beginner. In the proof, it says "Now it is clear that the sets A which satisfies the above relation form a monotone class." or "A second application of the theorem shows". But I am not sure how the theorem is applied rigorously.
Nov
12
comment Derivative of trace of a matrix
You can see the matrix cookbook.
Nov
12
revised Independence in infinite sequence of random variables
deleted 33 characters in body
Nov
12
comment Independence in infinite sequence of random variables
Thanks for the correction. Is it OK now?
Nov
12
revised Independence in infinite sequence of random variables
added 94 characters in body