Dear Team ,
Please provide solution for derivation of kolmogorov,s forward differential equation
i fail to under stand how Pij(t+h) = ∑ pik (t) pkj (h) = pij(t) + h ∑ pik (t) µkj + o (h)
as per my understanding:
Pij(t+h) = ∑ pik (t) pkj (h) --------------------------(1)
now pkj (h) is a transition from k to j state in small time interval h is given by formulae in chapter 5 page 16 equation 5.7 which is as follows :
pij(h) = {h µij + o (h) if i not equal to j and is 1+ h µij + o (h) if i = j
now we can substitute it in equation 1
Pij(t+h) = ∑ pik (t) pkj (h)
= ∑ pik (t) µkj + o (h)
please provide steps after this to derive the equation mentioned above.
regards
suresh sharma
Last edited by a moderator: Jun 12, 2017