## The Annals of Probability

### Circuit Processes

J. MacQueen

#### Abstract

Circuit processes of order $r$ are defined using a finite class of weighted circuits in a finite set $S$. The probability of the next value of the process is made proportional to the total weight of those circuits in the class which pass through the value in question and the last $r$ values. The process is an order $r$ Markov chain in $S$, and the stationary distribution is easily calculated. Also, it is shown that all stationary order $r$ Markov chains in a finite set can be represented as circuit processes of that order.

#### Article information

Source
Ann. Probab., Volume 9, Number 4 (1981), 604-610.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176994365

Digital Object Identifier
doi:10.1214/aop/1176994365

Mathematical Reviews number (MathSciNet)
MR624686

Zentralblatt MATH identifier
0464.60070

JSTOR