AP-frames and stationary random processes

It is known that, in general, an AP-frame is an L-2(R)-frame and conversely. Here, in part as a consequence of the Ergodic Theorem, we prove a necessary and sufficient condition for a Gabor system {g(t-k)e(il(t-k)),l is an element of L=omega(0)Z,k is an element of K=t(0)Z} to be an L-2(R)-Frame in terms of Gaussian stationary random processes. In addition, if X=(X(t))(t is an element of R )is a wide sense stationary random process, we study density conditions for the associated stationary sequences {<X,g(k,l)>, l is an element of L,k is an element of K}. (C) 2022 Elsevier Inc. All rights reserved.