Predictions and function spaces

Okay, let's assume we want to do a forecast of some kind of continuous stochastic process. One way we can do this is through the Wiener measure on C([0,inf)), but as far as I know, it looks like a BIG BITCH TO ME. So what I was thinking of instead was then defining a probability measure on the space of analytic functions so that, when you get your resulting probability distribution, you could maximize the probability distribution (functional) with the calculus of variations. The reason why I've chosen the space of analytic functions is because every function can be written in terms of a power series, so doing the maximizing could quite possibly reduce down to the selection of a denumerably infinite number of parameters--i.e., the coefficients of the power series. This would probably be easier than doing the calculus of variations straight up.

Thoughts?

BTW, the maximizing of the probability distribution functional would yield the function with the most probable path for the stochastic process.

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