TY - JOUR
T1 - Sofic random processes
AU - Krieger, Wolfgang
AU - Weiss, Benjamin
PY - 2012/10
Y1 - 2012/10
N2 - For a finite alphabet Σ, a subshift Y ⊂ Σ ℤ and an ergodic shift invariant probability measure with support Y, the future measures of the process (Y;n) are the conditional measures of v on the future, given the past. We introduce sofic processes as the processes that have finitely many future measures. We characterize the weighted Shannon graphs that canonically present sofic processes that are finitarily Markovian. With an example of Furstenberg as a starting point, we characterize the weighted Shannon graphs that canonically present sofic processes that are not finitarily Markovian. The semigroup measures of Kitchens and Tuncel yield sofic processes. We show that the class of sofic processes with semigroup measures is closed under measure preserving topological conjugacy.
AB - For a finite alphabet Σ, a subshift Y ⊂ Σ ℤ and an ergodic shift invariant probability measure with support Y, the future measures of the process (Y;n) are the conditional measures of v on the future, given the past. We introduce sofic processes as the processes that have finitely many future measures. We characterize the weighted Shannon graphs that canonically present sofic processes that are finitarily Markovian. With an example of Furstenberg as a starting point, we characterize the weighted Shannon graphs that canonically present sofic processes that are not finitarily Markovian. The semigroup measures of Kitchens and Tuncel yield sofic processes. We show that the class of sofic processes with semigroup measures is closed under measure preserving topological conjugacy.
UR - http://www.scopus.com/inward/record.url?scp=84870190697&partnerID=8YFLogxK
U2 - 10.1515/CRELLE.2011.164
DO - 10.1515/CRELLE.2011.164
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:84870190697
SN - 0075-4102
SP - 31
EP - 47
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 671
ER -