Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuous Disintegrations of Gaussian Processes   The goal of this paper is to understand the conditional law of a stochastic
process once it has been observed over an interval. To make this precise, we
introduce the notion of a continuous disintegration: a regular conditional
probability measure which varies continuously in the conditioned parameter. The
conditioning is infinite-dimensional in character, which leads us to consider
the general case of probability measures in Banach spaces. Our main result is
that for a certain quantity $M$ based on the covariance structure, the
finiteness of M is a necessary and sufficient condition for a Gaussian measure
to have a continuous disintegration. The condition is quite reasonable: for the
familiar case of stationary processes, M = 1.

37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
19
The categories of this paper are: eess