# Continuous Time Stochastic Process

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!

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If you did'nt study any stochastic processes maybe you should start out with something simpler ... or you could try to simulate (program) your process on a computer and see ... – kjetil b halvorsen Sep 27 '12 at 7:46
I already have computer simulations (using Gillespie algorithm), what I'd like to find in a theoretical estimate of what I see from the simulations... – lucacerone Sep 27 '12 at 11:11

Don't have the time to solve your problem explicitly, but I think I can put you on the right track. Your problem description sounds exactly like an Ising model, which is an extremely well studied class of models.

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yes it seems :) thanks a lot! – lucacerone Sep 27 '12 at 21:25