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F. Bracci, M.D. Contreras, S. D\'iaz Madrigal proved that any evolutionfamily 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 substitutionwhich transforms it to an It\^o diffusion.We generalize their result to vectorrandomized Loewner chain and prove there are no other possibilities totransform such Loewner chains to It\^o diffusions.

Loewner Evolution as It\^o Diffusion