We use wavelet-type discrete transforms for signal analysis on strings of finite length. We apply these transforms for edge and hidden Markov process detection. We also present new approaches for string matching and for measures of the diversity of chaotic strings.
Let a Poisson process be observed whose output rate is one of two levels given by the state of an unseen Markov process. If one of the levels is 0, a simple formula is given for the best guess of the state at any instant based on the stream of past Poisson events. In other cases bounds are given for the likelihood ratio of the state probabilities given the event stream.