Abstract
We prove the existence of an invariant measure for a large class of random processes with discrete time without assuming their linearity. Our main examples are “processes with variable length”, in which components may appear and disappear in the course of functioning. One of these examples displays non-uniqueness of invariant measure in a 1-D process.
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Toom, A. Every Continuous Operator Has an Invariant Measure. J Stat Phys 129, 555–566 (2007). https://doi.org/10.1007/s10955-007-9407-9
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DOI: https://doi.org/10.1007/s10955-007-9407-9