Kevin buckley 2007 markov sequences consider a

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: re easily characterized, statistically, than general random processes, and they occur commonly in nature and engineering system. Kevin Buckley - 2007 Markov Sequences: Consider a discrete-time random sequence Xn . If, for all K and n, p(xn /xn−1 , xn−2 , · · · , xn−K ) = p(xn /xn−1 ) , then Xn is a Markov sequence. For a Markov sequence, 2 (3) p(xn , xn−1 , xn−2 , · · · , xn−K ) = p(xn /xn−1 ) p(xn−1 /xn−2 ) · · · p(xn−K +1 /xn−K ) p(xn−K ) K −1 = p(xn−K ) k =0 p(xn−k /xn−k−1) . (4) Vector Markov Sequences: To this point we have discussed only scalar Markov processes X (t) and sequences Xn . This discussion generalizes to vector random processes and sequences. For example, let X n denote an L-dimensional vector random sequence. X n is a vector Markov sequence if, for all K and n, p(xn /xn−1 , xn−2 , · · · , xn−K ) = p(xn /xn−1 ) . Then p(xn , xn−1 , xn−2 , · · · , xn−K ) = p(xn /xn−1 ) p(xn−1 /xn−2 ) · · · p(xn−K +1/xn−K ) p(xn−K ) K −1...
View Full Document

This document was uploaded on 10/12/2009.

Ask a homework question - tutors are online