Hello everyone,(adsbygoogle = window.adsbygoogle || []).push({});

I am trying to figure out some overall possibilities of some states for a certain configuration and need a bit of help with probability theory.

So, assume that there is an object that can take 3 states {0, 1, 2} and the object can only change the state by doing one jump at a time. So, from 0 to 1 and then from 1 to 2 (I think it is called the Ising model)...

Initially the object is in state 0 and an event happens and the object can either stay in state 0 or move to state 1.

So, we have P_1(0) and P_1(1) and their sum is 1.

Now, consider the following scenario: object stayed in state (0). We have another event:

Again, we have a new set of probabilities

P_2(0) and P_2(1) again their sum is 1.

Now, after these two events, what is the overall probability that the object stays in state 0 or state 1?

Now, consider another scenario: object jumps to state (1) after the first event. Now, in the second event, we have probabilities

P_2(1) and P_2(2). So, it can either stay in state 1 or move to state 2.

So, overall what should be the probability of it being in state (0), (1) or (2)... is there a simple way to think about this that can encapsulate all these scenarios.

The background is that I am trying to code a small program that can track all the probabilities of these state jumps for this object and the problem is that the states can be more than 3...more like 20! And I want to figure out an algorithm and, of course, also understand how this probabilities evolve..

Would appreciate any help you can give me.

Thanks,

Luca

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# Need help with basic probability

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