I just came across something very similar while answering another MO question. In stochastic calculus [X,Y] is standard notation for quadratic covariations. Reading through the discussion of Hormander's in Rogers & Williams (Diffusions, Markov Processes, and Martingales), I see that, at the same time, [X,Y] is used for the Lie Bracket of vector fields. Confusing, especially for processes in the tangent space of a manifold. Not necessarily bad notation though, just a conflict when combining different fields of maths.

Wikipedia's entry for Poisson random measures which I linked to above is pretty bad. If you don't already know abut point processes, then this would be a better link - en.wikipedia.org/wiki/Point_process.

The measure preserving property is not relevant, because you can always replace mu(A) by sum_g mu(gA)

If X has finite p-variation and Y finite q-variation with 1/p+1/q=1, then you can use the Holder inequality rather than Cauchy-Schwartz in my argument above to get a bound on the correction term. If 1/p+1/q>1 then there will be no correction, and using a similar argument as with Riemann integration, the integral does exist. If 1/p+1/q <= 1 then we only have a bound on the correction term. There is no guarantee that the sum converges to a well defined integral but, if it does, there can be a correction correction term.

Added a couple of references. Both are only available in French though. Also, I noticed the same "unknown control sequence" problem, but it went away after refreshing the page. I see the correct formulas now both on my laptop and iphone, so it should be fine. If you're still getting the problem I'll change the notation.

Should this also have the pr.probability tag? I sometimes filter by that tag, and would expect to see questions such as this.

In that case, I think a(x) in V has to be of the form a(x)=b(x)(cos(k),-sin(k)) where b(x)k(x) is smooth, and it just reduces to the n=1 case. But that is the kind of thing I was thinking of.