I'm trying to solve the Kolmogorov backward equations for a Birth-Death Markov chain with three states. I have 2 equations:
$$P_{00}'(t) = \lambda_0 (P_{10}(t)-P_{00}(t))$$ $$P_{10}'(t) = \mu_1P_{00}(t)$$
do I understand it correctly that the forward equations will give the same results
EDIT I was able to confirm (numerically) the same results.
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