Lesson plan
Telegraph process
In probability theory, the telegraph process is a memoryless continuous-time stochastic process that shows two distinct values. It models burst noise (also called popcorn noise or random telegraph signal). If the two possible values that a random variable can take are c_1 and c_2 , then the process can be described by the following master equations: : \partial_t P(c_1, t|x, t_0)=-\lambda_1 P(c_1, t|x, t_0)+\lambda_2 P(c_2, t|x, t_0) and : \partial_t P(c_2, t|x, t_0)=\lambda_1 P(c_1, t|x, t_0)-\lambda_2 P(c_2, t|x, t_0). where \lambda_1 is the transition rate for going from state c_1 to state c_2 and \lambda_2 is the transition rate for going from going from state c_2 to state c_1 . The process is also known under the names Kac process (after mathematician Mark Kac), and dichotomous random process.
Article summary
In probability theory, the telegraph process is a memoryless continuous-time stochastic process that shows two distinct values. It models burst noise (also called popcorn noise or random telegraph signal). If the two possible values that a random variable can take are c_1 and c_2 , then the process can be described by the following master equations: : \partial_t P(c_1, t|x, t_0)=-\lambda_1 P(c_1, t|x, t_0)+\lambda_2 P(c_2, t|x, t_0) and : \partial_t P(c_2, t|x, t_0)=\lambda_1 P(c_1, t|x, t_0)-\lambda_2 P(c_2, t|x, t_0). where \lambda_1 is the transition rate for going from state c_1 to state c_2 and \lambda_2 is the transition rate for going from going from state c_2 to state c_1 . The process is also known under the names Kac process (after mathematician Mark Kac), and dichotomous random process.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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