New results are presented on the problem of source coding subject to a fidelity criterion for stationary, measurable, continuous-time stochastic processes. The main result is established without an ergodicity requirement and for quite general reproduction alphabets. This is then specialized to ergodic sources to prove a coding theorem for ergodic continuous-time sources. The approach is to obtain coding theorems for continuous-time sources from the coding theorem for nonergodic discrete-time sources.
"Source Coding Theorems for Stationary, Continuous-time Stochastic Processes." Ann. Probab. 5 (6) 966 - 986, December, 1977. https://doi.org/10.1214/aop/1176995664