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I came across a type of random process earlier with the structure $$ X(t) = (-1)^{N(t)}Y,\ t\geqslant 0 $$ where $\{N(t):t\geqslant 0\}$ is a homogeneous Poisson process with intensity $\lambda$ and $Y$ is a symmetric Rademacher random variable, i.e. $\mathbb P(Y=1)=1/2 = \mathbb P(Y=-1)$ independent of $\{N(t)\}$. It was called a random telegraph signal. Obviously $X(t)=\pm 1$ as according to the number of jumps in the Poisson process and $Y$ determines the value of $X(0)$.

Searching for "random telegraph signal," I could not find anything related to this type of process. I'm interested in literature (textbooks or papers) that study this process and its generalizations in more detail, but I do not know what to search for.

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  • $\begingroup$ en.wikipedia.org/wiki/Telegraph_process $\endgroup$ – George Dewhirst Nov 23 at 1:54
  • $\begingroup$ theres quite a few links to other pages there too $\endgroup$ – George Dewhirst Nov 23 at 1:55
  • $\begingroup$ search for "arxiv" and "random telegraph signal" ; and in google.books. search for "random telegraph signal" . Both yield plenty. $\endgroup$ – kimchi lover Nov 23 at 2:20
  • $\begingroup$ @GeorgeDewhirst I saw the Wikipedia article, but it didn't seem to be describing the same type of process. $\endgroup$ – Math1000 Nov 23 at 3:25
  • $\begingroup$ @kimchilover I did a quick search on arXiv and didn't find anything relevant. Perhaps there is a different name by which I should be searching? $\endgroup$ – Math1000 Nov 23 at 3:26

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