In a continuous-time Markov chain with state X(t) at time t, define p ij(t) as the probability that X(t + s) = j, given that X(s) = i, s, t ≥ 0, and r ij as the transition rate out of state i to state j. Then Kolmogorov's backward equations say that, for all states i, j and times t ≥ 0, the derivatives dp ij(t)/dt = Σk≠i r ik p kj(t) − v i p ij(t), where v i is the transition rate out of state i, v i = Σj r ij. Markov chains; Markov processes.
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© 2001 Kluwer Academic Publishers
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Gass, S.I., Harris, C.M. (2001). BACKWARD KOLMOGOROV EQUATIONS . In: Gass, S.I., Harris, C.M. (eds) Encyclopedia of Operations Research and Management Science. Springer, New York, NY. https://doi.org/10.1007/1-4020-0611-X_50
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DOI: https://doi.org/10.1007/1-4020-0611-X_50
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