Does anyone know how I can get an approximate structure for sovereign debt holders? I'm looking mostly into European countries. The type of info needed is what percentage of the German bonds are held by France and the other way around. Moreover, it would be good to be able to see how this type of st...

Thanks, that's a useful reference.

<t>By some old results of Schoenberg, for any times [$]t_1,t_2,\dots,t_n[$], the matrix with element [$]i,j[$] given by [$]\exp(-|t_i-t_j|^2)[$] is positive definite. If I am not mistaken, this is sufficient for the existence of a Gaussian stochastic process with auto-covariance function [$]\exp(-s^...

<t>On the first point we're just comparing guesses. My guess was that the probability of non-measurability was 0. Indeed it seems trivial to me that the integral of the function you describe is 0.5 with probability 1. But I may well be wrong.Your second point is worrying though. From the Wikipedia p...

<t>On the left hand side I presume you mean? U(i) is the realisation of the (standard) uniform random variable, so it's just an integral over an everywhere discontinuous function. Treating it as a Lebesgue integral is fine. In the case when f is not a function of i, by the Strong Law of Large number...

Well my intuition was that the integral on the left hand side was identical in all states of the world, by a law of large numbers style result and hence that it could be equal to the non-random right hand side.

I've just noticed there was a mistake in my description of the problem. f is also a function of i, so the actual question is whether:Thanks.

<t>Suppose for i in [0,1], U(i) is a uniformly distributed independent random variable.Am I right in thinking that for any continuous function f:where E is the expectation operator? (That is if these integrals are actually defined?) Is there a reference for this?I imagine it's a straight forward app...

<t>I should really have understood his original reply (sorry!), my background's not in finance/SDEs so perhaps it was a clash of language. I guess his obvious first sentence threw me into not reading the second close enough to realise he was making an argument about absolute continuity. But anyway, ...

Ahh right, sorry I understand you now. That does make perfect sense.Thanks.

<t>You understand the standard Cameron-Martin theorem right? In the standard case you have a random walk with drift mu, and you can "change measure" into one without drift. E.g. you move to a measure with drift.Your argument if I understand it would apply just as well to this case, so cannot be corr...

Oh well by "a Brownian Bridge with drift" I meant the path of W(s) given W(0)=0 and W(1)=x where x\ne 0.I can do the x=0 case, I'd like to be able to generalise to the x\ne 0 one.Thanks,Tom

<t>Hi,I'm trying to evaluate an expectation of a functional of the entire path of a Brownian Bridge (i.e. it contains an integral). By using a result I found in a paper I can evaluate this expectation when the Brownian Bridge does not have any drift, however I need to generalise it to the case with ...