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Chapman-Kolmogorov Equations

These are used to compute n-step transition probabilities as given by

for all i , j, n and 0 ≥ v n.

When                                      v = 1, then

for all i, j, n

When                                      v = n - 1, then

for all i, j, n

The above equations show that the n-step transition probabilities can be obtained from the one step transition probabilities recursively.

 

Let n = 2, then we can write

for all i, j, n

The above equations show that the n-step transition probabilities can be obtained from the one step transition probabilities recursively.

 

Let n = 2, then we can write