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A note on the asymptotic properties of correlated random walks
J. B. T. M. Roerdink
Journal:

Journal of Applied Probability / Volume 22 / Issue 4 / December 1985

Published online by Cambridge University Press:

14 July 2016, pp. 951-956

Print publication:

December 1985
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We describe a simple relation between the asymptotic behavior of the variance and of the expected number of distinct sites visited during a correlated random walk. The relation is valid for multistate random walks with finite variance in dimensions 1 and 2. A similar relation, valid in all dimensions, exists between the asymptotic behavior of the variance and of the probability of return to the origin.

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A note on the asymptotic properties of correlated random walks