Vadim A. Kaimanovich, Yuri Kifer, Ben-Zion Rubshtein
Boundaries and Harmonic Functions for Random Walks with Random Transition Probabilities
Preprint series: ESI preprints

MSC:

60J50 Boundary theory

60B99 None of the above but in this section

Abstract: The usual random walk on a group (homogeneous both in time and in space) is
determined by a probability measure on the group. In a random walk with random
transition probabilities this single measure is replaced with a stationary
sequence of measures, so that the resulting (random) Markov chains are still
space homogeneous, but no longer time homogeneous. We study various notions of
measure theoretical boundaries associated with this model, establish an
analogue of the Poisson formula for (random) bounded harmonic functions, and
identify these boundaries for several classes of groups.

Keywords: Random walk, random transition probability, harmonic function, Poisson boundary