An extension of a convergence theorem for Markov chains arising in population genetics
2016 ◽
Vol 53
(3)
◽
pp. 953-956
◽
Keyword(s):
AbstractAn extension of a convergence theorem for sequences of Markov chains is derived. For every positive integer N let (XN(r))r be a Markov chain with the same finite state space S and transition matrix ΠN=I+dNBN, where I is the unit matrix, Q a generator matrix, (BN)N a sequence of matrices, limN℩∞cN= limN→∞dN=0 and limN→∞cN∕dN=0. Suppose that the limits P≔limm→∞(I+dNQ)m and G≔limN→∞PBNP exist. If the sequence of initial distributions PXN(0) converges weakly to some probability measure μ, then the finite-dimensional distributions of (XN([t∕cN))t≥0 converge to those of the Markov process (Xt)t≥0 with initial distribution μ, transition matrix PetG and limN→∞(I+dNQ+cNBN)[t∕cN]
2009 ◽
Vol 46
(02)
◽
pp. 497-506
◽
2003 ◽
Vol 40
(1)
◽
pp. 107-122
◽
Keyword(s):
2003 ◽
Vol 40
(01)
◽
pp. 107-122
◽
Keyword(s):
2009 ◽
Vol 46
(2)
◽
pp. 497-506
◽
2009 ◽
Vol 46
(3)
◽
pp. 866-893
◽
1982 ◽
Vol 19
(02)
◽
pp. 272-288
◽
Keyword(s):
2008 ◽
Vol 45
(3)
◽
pp. 630-639
◽
Keyword(s):
2009 ◽
Vol 46
(03)
◽
pp. 866-893
◽
1994 ◽
Vol 8
(1)
◽
pp. 1-19
◽