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arXiv · 1505.04521

Loewner Evolution as It\^o Diffusion

Hülya Acar·Alexey L. Lukashov
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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.

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Hülya Acar, Alexey L. Lukashov. 2015-05-18. Loewner Evolution as It\^o Diffusion. https://doi.org/10.1063/5.0040353

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