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Aug
20
revised Number of ways to sample a specific number of objects from a collection with several types of objects.
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Aug
20
accepted Number of ways to sample a specific number of objects from a collection with several types of objects.
Aug
20
comment Number of ways to sample a specific number of objects from a collection with several types of objects.
Yep, that is really super simple, I'm not sure why I got so messed up with this... Counting problems have never been my strong suit. Thanks!
Aug
20
asked Number of ways to sample a specific number of objects from a collection with several types of objects.
Aug
4
awarded  Benefactor
Aug
4
comment Normalized hit times of a simple RW converge in distribution to hit times of standard Brownian Motion
Superb, this has been most informative :)
Aug
4
comment Normalized hit times of a simple RW converge in distribution to hit times of standard Brownian Motion
What do you learn from $cosh(\alpha S_{j})$ having deterministic value at the stopping time? Also there is one equality I don't quite understand, $E[(\frac{1}{\cosh\alpha})^{\tau_{n}}]=\frac{1}{\cosh(\alpha n)}$ Other than that, it is really a very deductive solution and I learnt quite a lot. Thank you again!
Aug
4
comment Normalized hit times of a simple RW converge in distribution to hit times of standard Brownian Motion
First of all, thanks a lot for the detailed solution. I do have one question, assuming one does not know what result to expect as the MGF of the process. How does one know to look at the process defined as $M_{j}$? It seems kind of like magic and I don't have any intuition as to why one would resolve to look at that specific process.
Aug
4
accepted Normalized hit times of a simple RW converge in distribution to hit times of standard Brownian Motion
Aug
1
comment Normalized hit times of a simple RW converge in distribution to hit times of standard Brownian Motion
@Calculon, I'm afraid that despite your kind attempts I simply don't know how to utilize them. If you're up to writing a detailed solution that would be extremely appreciated. If it's too much of a hassle I understand and thank you regardless.
Jul
30
comment Normalized hit times of a simple RW converge in distribution to hit times of standard Brownian Motion
I have to admit that I simply never saw how to use this sort of technique in order to find moment generating functions. So even though the hints are solid I just don't know how to implement them.
Jul
30
comment Normalized hit times of a simple RW converge in distribution to hit times of standard Brownian Motion
Hi Calculon, thanks for your reply. I thought about going in this direction but my problem is that I don't know what the pmf/pdf of the discrete/continuous hitting times are and without those I have no idea how to find the MGF.
Jul
30
asked Normalized hit times of a simple RW converge in distribution to hit times of standard Brownian Motion
Feb
27
revised Convergence of Conjugate Gradient Method for Positive Semi-Definite Matrix
added 1556 characters in body
Feb
26
comment Convergence of Conjugate Gradient Method for Positive Semi-Definite Matrix
Hey Murp, thanks for your reply! I'm afraid I wasn't able to find any useful way to use the spectral decomposition of $A$ in order to prove these properties (no idea why it was given as a hint), I was however able to additionally prove that the error is monotonically decreasing in the $A$-norm, I will add that to my post later today.
Feb
26
accepted Convergence of Conjugate Gradient Method for Positive Semi-Definite Matrix
Feb
16
awarded  Promoter
Feb
15
revised Convergence of Conjugate Gradient Method for Positive Semi-Definite Matrix
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Feb
15
revised Convergence of Conjugate Gradient Method for Positive Semi-Definite Matrix
correction to update formula
Feb
15
revised Convergence of Conjugate Gradient Method for Positive Semi-Definite Matrix
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