represents a telegraph process with rate μ.
- TelegraphProcess is a continuous-time and discrete-state random process.
- TelegraphProcess at time t takes the value 1 if the number of events in the interval 0 to t is even and -1 otherwise.
- The number of events in the interval 0 to t follows PoissonDistribution[μ t].
- The times between events are independent and follow ExponentialDistribution[μ].
- TelegraphProcess allows μ to be any positive real number.
- TelegraphProcess can be used with such functions as Mean, PDF, Probability, and RandomFunction.
Examplesopen allclose all
Basic Examples (3)
Basic Uses (6)
Process Slice Properties (6)
CentralMoment and its generating function:
FactorialMoment and its generating function:
The collision times for a particle moving between two barriers are distributed exponentially, with a mean of 3 microseconds. If the particle starts at the right-hand barrier () and moves towards the left-hand barrier (), then simulate the collision process for 100 microseconds:
Properties & Relations (6)
TelegraphProcess is a jump process:
The number of jumps at time t follows a PoissonDistribution:
The times between jumps follow an ExponentialDistribution:
Wolfram Research (2012), TelegraphProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/TelegraphProcess.html.
Wolfram Language. 2012. "TelegraphProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/TelegraphProcess.html.
Wolfram Language. (2012). TelegraphProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TelegraphProcess.html