Some explicit results for correlated random walks
1989 ◽
Vol 26
(04)
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pp. 757-766
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Keyword(s):
In a correlated random walk (CRW) the probabilities of movement in the positive and negative direction are given by the transition probabilities of a Markov chain. The walk can be represented as a Markov chain if we use a bivariate state space, with the location of the particle and the direction of movement as the two variables. In this paper we derive explicit results for the following characteristics of the walk directly from its transition probability matrix: (i) n -step transition probabilities for the unrestricted CRW, (ii) equilibrium distribution for the CRW restricted on one side, and (iii) equilibrium distribution and first-passage characteristics for the CRW restricted on both sides (i.e., with finite state space).
1988 ◽
Vol 1
(3)
◽
pp. 197-222
2018 ◽
Vol 55
(3)
◽
pp. 862-886
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2004 ◽
Vol 36
(4)
◽
pp. 1198-1211
◽
1968 ◽
Vol 5
(01)
◽
pp. 220-223
◽
1982 ◽
Vol 19
(03)
◽
pp. 685-691
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