I'm wondering if anyone knows of a reasonably rigorous text on stochastic processes that discusses specifically things like the autocorrelation, spectral density, and other "correlation and spectral" properites of stochastic processes. It seems like many rigorous mathematical probability & stochastic books (e.g. Karatzas & Shreve) don't seem to employ these tools whatsoever, while engineering texts (like Papoulis) seem to favor them heavily. Is there any reason for this difference, and do any interesting mathematical texts on stochastic processes make use of these tools?

  • $\begingroup$ You may want to look at Ash and Gardner's "Topics in Stochastic Processes." These topics are covered rigorously, though perhaps not in the level of generality you might want for all applications. $\endgroup$ – Chris Janjigian Jan 15 '16 at 20:09
  • $\begingroup$ Grimmett and Stirzacker has some material. I don't know whether it's what you wanted. $\endgroup$ – Mars Feb 8 at 4:40

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