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Jan
27
comment Polytopes defined by $x_i >=0, Ax = b$ are generic ? (Understanding simplex method)
Thank you again, however that differs in tiny (but important) detail from what I am asking. I am asking weaker thing: all vertices have AT LEAST (n-r) zero components (I allow to have more zero components) - is it true ? Well, actually it seems "obvious", but I want to check that my understanding is correct.
Jan
27
comment Polytopes defined by $x_i >=0, Ax = b$ are generic ? (Understanding simplex method)
Thank you. Yeh, you right. something like (-x = b) is not consistent with x > 0. So there should be at most C(r,n), but not exactly C(r,n). However is it true that all vertices can be described "as points (x1...xn) with n−r coordinates equal to zero,"
Jan
24
asked Polytopes defined by $x_i >=0, Ax = b$ are generic ? (Understanding simplex method)
Jan
17
comment Iterated logarithm law for difference (supremum(W) - infimum(W) ) is it 2srt(2/pi) sqrt(t loglog(t))?
Sorry, "counterexample" is incorrect , i was keeping in mind the lim(sup-inf), but writing about E(sup-inf). So to conclude your argument perfectly explains the matlab code result. Thank you. Still I am interstring about log-log-law, but clearly my proposed is incorrect.
Jan
15
comment Iterated logarithm law for difference (supremum(W) - infimum(W) ) is it 2srt(2/pi) sqrt(t loglog(t))?
My "counterexample" to the formula is the following - consider random process such that trajectories may have only the following form x(n) = 0, for all "n" except only one position, at that position "trajectory" may have a value +1 or -1. with equal probability. So for time n<=K, we have only 2K trajectories. Then clearly the formula is not correct. What does it mean ? Does it mean that not all measures on trajectories corresponds to random processes in mathematical sense or something else ?
Jan
15
comment Iterated logarithm law for difference (supremum(W) - infimum(W) ) is it 2srt(2/pi) sqrt(t loglog(t))?
well may be you are right, let me think, but that formula seems contrintuitive for me. Is this formula true in discrete case for sum of two iid ? where "trajectory" is set of two points x_1 , x_1+x_2 ? so max is max(x_1,x_1+x_2) and min of that expression ... Well seems it is true just because E(a+b) =E(a)+E(b) ... well sometimes formal approach gives faster answers than "intuitive". I think a little more ...
Jan
15
comment Iterated logarithm law for difference (supremum(W) - infimum(W) ) is it 2srt(2/pi) sqrt(t loglog(t))?
I am not sure my explanation is clear. But may be you catch the idea. Any way I should write a code to compare with your way of calculation - then it would be clear what I mean from the code...
Jan
15
comment Iterated logarithm law for difference (supremum(W) - infimum(W) ) is it 2srt(2/pi) sqrt(t loglog(t))?
How do you think about "E" - my way of thinking is "sum over trajectories", any way, in discrete case (random work) this is indeed the formally correct. So we take trajectory and calculate max-min for fixed trajectory - exactly this is done in my matlab code. It is not the same as take max, then sum over trajectories.
Jan
15
comment Iterated logarithm law for difference (supremum(W) - infimum(W) ) is it 2srt(2/pi) sqrt(t loglog(t))?
About "does your answer explain the matlab result" - I have the following question - look you write: "the running minimum is just the negative of that . Hence the formula you used" . It seems it supposes that E(Max-Min) = E(Max) - E(Min) , but that does not seems for me to be true. Because ...
Jan
15
comment Iterated logarithm law for difference (supremum(W) - infimum(W) ) is it 2srt(2/pi) sqrt(t loglog(t))?
Thank you very much for your helpful answer. You right that matlab code does not check exactly the same formula which i propose. However two question arises 1) does your answer explain matab result 2) is the proposed formula true anyway
Jan
14
awarded  Custodian
Jan
14
reviewed Edit Iterated logarithm law for difference (supremum(W) - infimum(W) ) is it 2srt(2/pi) sqrt(t loglog(t))?
Jan
14
revised Iterated logarithm law for difference (supremum(W) - infimum(W) ) is it 2srt(2/pi) sqrt(t loglog(t))?
LaTeX.........
Jan
14
asked Iterated logarithm law for difference (supremum(W) - infimum(W) ) is it 2srt(2/pi) sqrt(t loglog(t))?
Mar
20
awarded  Curious
Mar
3
asked How many unordered N-seqences in M letter alphabet?
Mar
31
awarded  Popular Question
Jun
30
comment Reference request for the law of the stopping time in the gambler's ruin problem
mathoverflow.net/questions/133399/… related
Jun
29
awarded  Yearling
Jan
1
comment What is the trellis diagram for a linear block code?
@JyrkiLahtonen Lahtonen Notifier: May I kindly ask you to look at mathoverflow.net/questions/117505/… PS Happy new year !