Markov chains in a stratified environment. (English) Zbl 1372.60102
Summary: We establish a recurrence criterion for a model of inhomogeneous random walk in \(\mathbb Z^{d+1}\) in environment stratified by parallel affine hyperplanes. The asymptotics of the random walk is governed by some notion of directional flux variance, describing the dispersive power of some associated average flow. Some examples are presented, as well as a geometric interpretation of the criterion, in relation with the level lines of some diffusion picture.
MSC:
| 60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |
| 60K20 | Applications of Markov renewal processes (reliability, queueing networks, etc.) |
References:
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