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- W2389156838 abstract "Let E= {0, 1, 2, …}, and P(k)= (p_(ij)(k))_(i, j∈E), k=1, 2, …, be a sequence of transition probability matrices. Suppose that ∑ k≥1 ∑ j≥1 p_(ij) (k) ≤1. Define E_0={0}∪{(k, i): k, i≥1} p_((l, i), (k, j))=δ_(lK)p_(ij)(k), l, k, i, j≥1, p_((l, i),0)=p_(i0) (1), p_(l, i)=p_(0i) (1), l, i≥1. p_(O0)=1-∑ k≥1 ∑ j≥1 p_(Oj) (k). Then P= (p_(μv))_(μ, v∈E). is called the one-point connection of P (k), k≥1. It is shown that P is irreducible, recurrent or nonrecurrent iff each of P(k), k≥1, is irreducibly, recurrent or nonrecurrent respectively. In the nonrecurrent case, the probability that the Markov chain tends to infinity along the k-th branch starting from the state 0 is equal to ∑ j≥1 p_(Oj)(k) (1-f_(jO) (k)) / ∑ k≥1 ∑ j≥1 p_(Oj) (k) (1-f_(jO)(k)) Hence, the quantity sup ∑ j≠i p_(ij)(1-f_(ji)) can be considered as the degree of nonrecurrence of Markov chains. The one-point connection of a sequence of Q-matrices is discussed in similar manner" @default.
- W2389156838 created "2016-06-24" @default.
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- W2389156838 date "1988-01-01" @default.
- W2389156838 modified "2023-09-28" @default.
- W2389156838 title "ONE-POINT CONNECTION OF MARKOV CHAINS" @default.
- W2389156838 hasPublicationYear "1988" @default.
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