What business cases are there for using Markov chains? I've seen the sort of play area of a markov chain applied to someone's blog to write a fake post. I'd like some practical examples though? E.g. useful in business or prediction of stock market, or the like...
Edit: Thanks to all who gave examples, I upvoted each one as they were all useful.
Edit2: I selected the answer with the most detail as the accepted answer. All answers I upvoted.
There is a class of optimization methods based on Markov Chain Monte Carlo (MCMC) methods. These have been applied to a wide variety of practical problems, for example signal & image processing applications to data segmentation and classification. Speech & image recognition, time series analysis, lots of similar examples come out of computer vision and pattern recognition.