A question about John Baez's definition of "stochastic Petri nets".

Question

John Baez, in his blog posts, introduces stochastic Petri nets as a Petri net that contains an additional function which maps each transition in the set of transitions $T$ to a real number. This function is called the "rate constant".

On the other hand, Wikipedia defines stochastic Petri nets as one that has an additional function which maps each transition to a random variable. This function models the (probabilistic) after which a transition will "fire".

I see the connection between the two: the "rate constant" function in the definition Baez supplies represents the "time averaged" output of a transition which in Wikipedia's definition has some probabilistic delay.

How can Baez's definition of a Petri net still be called "stochastic" if it is a deterministic approximation of a stochastic Petri net?

Answer 1

Baez's blog post here answers my question.

Then the probability that a given transition occurs in a short time $\Delta t$ is approximately:

• the rate constant for that transition, times

• the time t, times

• the number of ways the transition can occur.