# Reference request: Random telegraph signals.

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.

• en.wikipedia.org/wiki/Telegraph_process – George Dewhirst Nov 23 at 1:54
• theres quite a few links to other pages there too – George Dewhirst Nov 23 at 1:55
• search for "arxiv" and "random telegraph signal" ; and in google.books. search for "random telegraph signal" . Both yield plenty. – kimchi lover Nov 23 at 2:20
• @GeorgeDewhirst I saw the Wikipedia article, but it didn't seem to be describing the same type of process. – Math1000 Nov 23 at 3:25
• @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? – Math1000 Nov 23 at 3:26