I am trying to build a stochastic model where two processes happen randomly with different rates that depend on the status of the system.
Imagine you have a grid NxN made of 0 or 1.
The 1 elements turn into 0 with a constant rate $\lambda_1$.
The 0 elements that are adjacent to at least 1 element turn into 1 with a rate $\lambda_0$.
I would like to study this process, but as I have no background in stochastic processes, I find this quite complicated.
I have to finde the average number of 1s at time $t$.
Thanks in advance for the hints!