<r>When I mentioned better ways (compared to the simple Brownian bridge method just described) I was thinking of things like <URL url="http://dx.doi.org/10.1016/j.jco.2007.06.001">http://dx.doi.org/10.1016/j.jco.2007.06.001</URL> (this may be one of the "sorting methods" you talk about) or using the...

<r>Quote1. if i have 1000 simulation paths, 12 time steps and 3 underlyings, this would require 1000 36-D points from the low discrepancy sequence?That's right, for each simulation you need 12*3=36 independent numbers, now you have to generate three 12-step correlated paths using this numbers someho...

<t>The dimension of your problem is [number of steps]*[number of assets]; in your three-asset one-step example you'll need to generate N 3-D points of the low-discrepancy sequence. To use the sequence efficiently, you want the lower dimensions to have a bigger effect on your paths than the higher di...

<t>QuoteOriginally posted by: wileyswyour way of counting is already simple enough.i can give you a different reasoning: note the fact that if 3 ppl sit around a table, the probability is 1 that they sit in order of age. if you add another person, ....You can also calculate the probability sequentia...

<t>QuoteOriginally posted by: twofishThat I think is the problem in that the results that I'm getting seem to indicate that case 2 is equivalent to case 1. The basic issue is that if you have two sources of radiation going in opposite directions, do you have a net energy transfer?If these opposite f...

Very close to one

<t>QuoteOriginally posted by: twofishI'm saying that the direction of energy transfer is going to be the same [...]I understand that the question is about the influx of solar radiation on the Earth surface, and I agree that the net direction is radial from the center of the Sun but I don't think it ...

<t>QuoteOriginally posted by: twofishSo the result of this is that if the source is spherically symmetrical the radiation field is going to be exactly the same, and so you can replace any spherically symmetric source with a point object and get the same radiation field.I might be misinterpreting you...

<t>QuoteOriginally posted by: quantystThe Actual Case A: Radiation from every point of the Sun is projected outward in a uniform fashion.Could you be more precise? If "projected outward in a uniform fashion" means that each point on the surface emits radiation isotropically on the positive hemispher...

<t>QuoteOriginally posted by: NicolasQuantyour corrective factor with the x (second image) seems to be equivalent to 1 as x-->0to my mind, the corrective factor for the punctual sun case should be below 1 (less than half of the Earth surface sees the sun) then equal to 1 around the case R=r (half of...

<t>QuoteOriginally posted by: quantystHow much of the original energy E is captured by the Earth? That is the question. The answer has nothing to do with the radius R of the Sun. In fact the answer has nothing to do with the shape of the Earth at all, but has everything to do with the ANGLE of the r...

<t>QuoteOriginally posted by: NicolasQuantTo get back to the brainteaser, I think you will agree with me that the exact answer has a dependance in R.I do agree there is a dependence, but found a different solution :-)In the r=0 limit (i.e. r is much smaller than R and D) I obtained Expressing R as a...

QuoteOriginally posted by: freakonlashI got the radiation asfor r << DIs it correct??I think you didn't apply correctly the Taylor expansion around x=0sqrt(1+x)=1+x/2-(x^2)/8+(x^3)/16....in this case 1-sqrt(1-x^2) can be approximated by (x^2)/2and your final result will be E/4*(r/D)^2

<t>QuoteOriginally posted by: quantystE[m/M]=...=E[X(1)/X(n) | X(1)<X(2)<...<X(n)] =E[E[X(1)/X(n) | X(1)<X(2)<...<X(n), X(n)] | X(1)<X(2)<...<X(n)]=E[(1/X(n)) E[X(1) | X(1)<X(2)<...<X(n), X(n)] | X(1)<X(2)<...<X(n)].This corresponds exactly to my second solution. I'm sorry if my notation was not cle...

<r>I found another proof, but I wouldn't say it is simpler!We can write the expectation E(m/M) as E(E(m/M|M))=E(1/M*E(m|M)), i.e. the expectation over M of the conditional expectation for M fixed.E(m|M) is the expectation of the minimum of (n-1) uniform variables in [0,M]. This minimum is distribute...