Dear Marshall,
Most of the notices that appear on this list are announcements, so it doesn’t seem appropriate to ask detailed, non-expert questions here. I hope you don’t mind if I ask a more meta-level question.
Is there an appropriate place for asking mathematical IP questions? Another mailing list?
Asking questions here is appropriate, I think. However, there is also a SIPTA Q&A site: <http://sipta.org/qa/>. But I do not know whether it is still maintained. The maintainers read this list, so they'll respond. As I seem to have lost my account details there, I'll give a quick answer to your question here. If needed we can continue on the Q&A site later.
math.stackexchange.com stats.stackexchange.com mathoverflow.net
I think all three can be appropriate, depending on the type of question. Perhaps the community could decide to use the Stack Exchange sites if maintaining and using its own Q&A site is too burdensome. But then we'd need to create a tag in those and have IP people follow that, or have an automated mail be sent here whenever a new question with the ‘imprecise probability’ tag appears there. Let's wait to see what the SIPTA Q&A maintainers think.
[In case it’s helpful, to illustrate the level of question I want to be able ask, here is the question with which I’m currently struggling: I’m reading Hermans and Skulj’s “Stochastic processes” chapter of of Introduction to Imprecise Probabilities, and I’m puzzled by the novel (to me) definition of “transition operator” in 11.3. I understand that it’s intended as a sort of generalization of the standard Markov process transition operator concept, but there’s something I’m just not seeing due to lack of experience, lack of insight, etc.: As I understand definition 11.3, T_n f(x) is essentially a conditional expectation—i.e., in traditional notation: E( f | X_n = x). How is it that T_n can operate on f(x) and “see” what x is? Either I must take 11.3 to imply that the domain of T_n consists of the range of f, or that the domain of T_n consists of gambles f in L(X_n). Either way, x does not seem to appear as an argument to T_n; it seems to “know” nothing about x. If the first interpretation were correct, then if f was not one-to-one, f(x) could equal f(y) where x != y, and I see no reason to assume that E(f | X_n=x) must always equal E(f | X_n=y). I’m not sure if I’m making myself clear; I’m sure that there’s something I've overlooked, or that I’m misinterpreting some notation or concept.]
T_n is an operator that maps gambles to gambles. So T_n f or T_n(f) returns a gamble. For example, g. So T_n f(x) = g(x) = (T_n f)(x) = E(f|X_n=x). So indeed, as you state “the domain of T_n consists of gambles f in L(X_n)”, but also the range of T_n consists of gambles g in L(X_n).
Best,
Erik