  F. Bracci, M.D. Contreras, S. D\'iaz Madrigal proved that any evolution
family of order d is described by a generalized Loewner chain. G. Ivanov and A.
Vasil'ev considered randomized version of the chain and found a substitution
which transforms it to an It\^o diffusion.We generalize their result to vector
randomized Loewner chain and prove there are no other possibilities to
transform such Loewner chains to It\^o diffusions.
