Loewner Evolution as It\^o Diffusion

Loewner Evolution as It\^o Diffusion

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...

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Hauptverfasser: Acar, Hülya, Lukashov, Alexey L
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Complex Variables
Mathematics - Probability
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Zusammenfassung: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.
DOI:10.48550/arxiv.1505.04521