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I wanted to find out what kind of different usages of stochastic processes theory in EE & CS are out there. For example, I find these kinds of usages interesting:

  • using stochastic signal as carrier that is modulated by the information signal for communication
  • using stochastic process analysis for improving photographed pictures after long exposition

It would be good if every example would be in separate answer, so it would be possible to up-vote those that are 'the best'. I would classify good example as one that:

  • truly takes advantage of probability and statistics theory
  • has greater 'usefulness' then other examples
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What about monitoring network congestion. An underlying stochastic process is assumed to be driving the congestion, and the process has reached an equilibrium state and is stationary. That is, process characteristics such as the mean level does not depend on time. You can then use this the stochastic process to give you an idea of when you check the network for possible congestion.

Some recent papers:

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Google's Pagerank algorithm is a stochastic approximation (through Markov's stationary state) of the proportion of visits received asymptotically by website $x_i$.

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As you have alluded to, communications engineering (and signal processing in general) is filled with stochastic processes. See, for example:

This is only two textbook examples. You will find many (many) more. It's fair to say that your mobile phone, the internet and etcetera all rely extremely heavily on our understanding of stochastic processes.

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