Infinite-Dimensional Measure Spaces and Frame Analysis

We study certain infinite-dimensional probability measures in connection with frame analysis. Earlier work on frame-measures has so far focused on the case of finite-dimensional frames. We point out that there are good reasons for a sharp distinction between stochastic analysis involving frames in finite vs. infinite dimensions. For the case of infinite-dimensional Hilbert space ?, we study three cases of measures. We first show that, for ? infinite dimensional, one must resort to infinite dimensional measure spaces which properly contain ?. The three cases we consider are: (i) Gaussian frame measures, (ii) Markov path-space measures, and (iii) determinantal measures.