Using a simplification of the notation in the paper, consider variance of the recursive relationship:
0) c(n) = u(n) + c(n-1) - c(n-1) u(n)
for n=1,2,... and c(0)=0. All c(n) and u(n) values represent probabilities i.e. lie with [0,1]. Furthermore, in the above expression (0), u(n) and c(n-1) are independent.
In evaluating the variance of (0), the indices are rather meaningless, as we are completely focused on the right hand side of the equation. I only include them in case a reader has access to the paper. The variance of (0) is presented as:
1) var c(n) = var u(n) + var C(n-1) + var[ c(n-1) u(n) ] - 2 cov[ u(n) , c(n-1) ] - 2 cov[ c(n-1) , c(n-1) u(n) ]
According to the above wikipedia page, however, it should be: