Löwner evolution as Itô diffusion

Hülya Acar; Alexey L. Lukashov

doi:10.1063/5.0040353

Löwner evolution as Itô diffusion

Hülya Acar, Alexey L. Lukashov^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

F. Bracci, M.D. Contreras, S. Díaz Madrigal [3] proved that any evaluation family of order d is described by a generalized Löwner chain. G. Ivanov and A. Vasil'ev considered randomized version of the chain and found a substitution which transforms the chain to an Itô diffusion. We generalize their result to vector randomized Löwner chain and prove there are no other possibilities to transform such Löwner chains to Itô diffusions.

Original language	English
Title of host publication	International Conference on Analysis and Applied Mathematics, ICAAM 2020
Editors	Allaberen Ashyralyev, Allaberen Ashyralyev, Allaberen Ashyralyev, Charyyar Ashralyyev, Abdullah S. Erdogan, Alexey Lukashov, Alexey Lukashov, Makhmud Sadybekov
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735440692
DOIs	https://doi.org/10.1063/5.0040353
Publication status	Published - 9 Feb 2021
Externally published	Yes
Event	5th International Conference on Analysis and Applied Mathematics, ICAAM 2020 - Mersin, Turkey Duration: 23 Sept 2020 → 30 Sept 2020

Publication series

Name	AIP Conference Proceedings
Volume	2325
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	5th International Conference on Analysis and Applied Mathematics, ICAAM 2020
Country/Territory	Turkey
City	Mersin
Period	23/09/20 → 30/09/20

Bibliographical note

Publisher Copyright:
© 2021 Author(s).

Access to Document

10.1063/5.0040353

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Acar, H., & Lukashov, A. L. (2021). Löwner evolution as Itô diffusion. In A. Ashyralyev, A. Ashyralyev, A. Ashyralyev, C. Ashralyyev, A. S. Erdogan, A. Lukashov, A. Lukashov, & M. Sadybekov (Eds.), International Conference on Analysis and Applied Mathematics, ICAAM 2020 Article 020004 (AIP Conference Proceedings; Vol. 2325). American Institute of Physics Inc.. https://doi.org/10.1063/5.0040353

Acar, Hülya ; Lukashov, Alexey L. / Löwner evolution as Itô diffusion. International Conference on Analysis and Applied Mathematics, ICAAM 2020. editor / Allaberen Ashyralyev ; Allaberen Ashyralyev ; Allaberen Ashyralyev ; Charyyar Ashralyyev ; Abdullah S. Erdogan ; Alexey Lukashov ; Alexey Lukashov ; Makhmud Sadybekov. American Institute of Physics Inc., 2021. (AIP Conference Proceedings).

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title = "L{\"o}wner evolution as It{\^o} diffusion",

abstract = "F. Bracci, M.D. Contreras, S. D{\'i}az Madrigal [3] proved that any evaluation family of order d is described by a generalized L{\"o}wner chain. G. Ivanov and A. Vasil'ev considered randomized version of the chain and found a substitution which transforms the chain to an It{\^o} diffusion. We generalize their result to vector randomized L{\"o}wner chain and prove there are no other possibilities to transform such L{\"o}wner chains to It{\^o} diffusions.",

author = "H{\"u}lya Acar and Lukashov, {Alexey L.}",

note = "Publisher Copyright: {\textcopyright} 2021 Author(s).; 5th International Conference on Analysis and Applied Mathematics, ICAAM 2020 ; Conference date: 23-09-2020 Through 30-09-2020",

year = "2021",

month = feb,

day = "9",

doi = "10.1063/5.0040353",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

editor = "Allaberen Ashyralyev and Allaberen Ashyralyev and Allaberen Ashyralyev and Charyyar Ashralyyev and Erdogan, {Abdullah S.} and Alexey Lukashov and Alexey Lukashov and Makhmud Sadybekov",

booktitle = "International Conference on Analysis and Applied Mathematics, ICAAM 2020",

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Acar, H & Lukashov, AL 2021, Löwner evolution as Itô diffusion. in A Ashyralyev, A Ashyralyev, A Ashyralyev, C Ashralyyev, AS Erdogan, A Lukashov, A Lukashov & M Sadybekov (eds), International Conference on Analysis and Applied Mathematics, ICAAM 2020., 020004, AIP Conference Proceedings, vol. 2325, American Institute of Physics Inc., 5th International Conference on Analysis and Applied Mathematics, ICAAM 2020, Mersin, Turkey, 23/09/20. https://doi.org/10.1063/5.0040353

Löwner evolution as Itô diffusion. / Acar, Hülya; Lukashov, Alexey L.
International Conference on Analysis and Applied Mathematics, ICAAM 2020. ed. / Allaberen Ashyralyev; Allaberen Ashyralyev; Allaberen Ashyralyev; Charyyar Ashralyyev; Abdullah S. Erdogan; Alexey Lukashov; Alexey Lukashov; Makhmud Sadybekov. American Institute of Physics Inc., 2021. 020004 (AIP Conference Proceedings; Vol. 2325).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Lukashov, Alexey L.

PY - 2021/2/9

Y1 - 2021/2/9

N2 - F. Bracci, M.D. Contreras, S. Díaz Madrigal [3] proved that any evaluation family of order d is described by a generalized Löwner chain. G. Ivanov and A. Vasil'ev considered randomized version of the chain and found a substitution which transforms the chain to an Itô diffusion. We generalize their result to vector randomized Löwner chain and prove there are no other possibilities to transform such Löwner chains to Itô diffusions.

AB - F. Bracci, M.D. Contreras, S. Díaz Madrigal [3] proved that any evaluation family of order d is described by a generalized Löwner chain. G. Ivanov and A. Vasil'ev considered randomized version of the chain and found a substitution which transforms the chain to an Itô diffusion. We generalize their result to vector randomized Löwner chain and prove there are no other possibilities to transform such Löwner chains to Itô diffusions.

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U2 - 10.1063/5.0040353

DO - 10.1063/5.0040353

M3 - Conference contribution

AN - SCOPUS:85101635272

T3 - AIP Conference Proceedings

BT - International Conference on Analysis and Applied Mathematics, ICAAM 2020

A2 - Ashyralyev, Allaberen

A2 - Ashralyyev, Charyyar

A2 - Erdogan, Abdullah S.

A2 - Lukashov, Alexey

A2 - Sadybekov, Makhmud

PB - American Institute of Physics Inc.

T2 - 5th International Conference on Analysis and Applied Mathematics, ICAAM 2020

Y2 - 23 September 2020 through 30 September 2020

ER -

Löwner evolution as Itô diffusion

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