Loewner Evolution as It\^o Diffusion
Complex Variables
2024-06-19 v1 Probability
Abstract
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.
Cite
@article{arxiv.1505.04521,
title = {Loewner Evolution as It\^o Diffusion},
author = {Hülya Acar and Alexey L. Lukashov},
journal= {arXiv preprint arXiv:1505.04521},
year = {2024}
}