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Unformatted text preview: General method
to find a formula for pij and any states i, j:
(n) for any M -state chain a) Compute the eigenvalues 1, 2, . . . , M of P by solving the characteristic equation; b) If the eigenvalues are distinct then pij has the form pij
(n) (n) = a1 1 n + + aM M n for some constants a1, . . . , aM (depending on i and j). If an eigenvalue is repeated (once, say) then the general form includes the term (a + bn)n. c) As roots of a polynomial with real coefficients, complex eigenvalues will come in conjugate pairs and these are best written using cos and sin . ...
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This note was uploaded on 05/12/2010 for the course APPLIED ST 2010 taught by Professor Various during the Spring '10 term at Universidad Nacional Agraria La Molina.
- Spring '10