Stochastic Komatu–Loewner evolutions and SLEs

Zhen Qing Chen; Masatoshi Fukushima; Hiroyuki Suzuki

doi:10.1016/j.spa.2016.09.006

Stochastic Komatu–Loewner evolutions and SLEs

Zhen Qing Chen^*, Masatoshi Fukushima, Hiroyuki Suzuki

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

A stochastic Komatu–Loewner evolution SKLE_α,b has been introduced in Chen and Fukushima (2016) on a standard slit domain determined by certain continuous homogeneous functions α and b. We show that after a suitable reparametrization, SKLE_α,b has the same distribution as the chordal Loewner evolution on H driven by a continuous semimartingale. When α is constant, we show that the distribution of SKLE_α,b, after a suitable reparametrization and up to some random hitting time, is equivalent to that of SLE_α². Moreover, a reparametrized SKLE_{6,−b_BMD} has the same distribution as SLE₆ for BMD domain constant b_BMD.

Original language	English
Pages (from-to)	2068-2087
Number of pages	20
Journal	Stochastic Processes and their Applications
Volume	127
Issue number	6
DOIs	https://doi.org/10.1016/j.spa.2016.09.006
Publication status	Published - 1 Jun 2017
Externally published	Yes

Keywords

Absorbing Brownian motion
Locality
SLE
Standard slit domain
Stochastic Komatu–Loewner evolution

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10.1016/j.spa.2016.09.006

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Chen, Z. Q., Fukushima, M., & Suzuki, H. (2017). Stochastic Komatu–Loewner evolutions and SLEs. Stochastic Processes and their Applications, 127(6), 2068-2087. https://doi.org/10.1016/j.spa.2016.09.006

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title = "Stochastic Komatu–Loewner evolutions and SLEs",

abstract = "A stochastic Komatu–Loewner evolution SKLEα,b has been introduced in Chen and Fukushima (2016) on a standard slit domain determined by certain continuous homogeneous functions α and b. We show that after a suitable reparametrization, SKLEα,b has the same distribution as the chordal Loewner evolution on H driven by a continuous semimartingale. When α is constant, we show that the distribution of SKLEα,b, after a suitable reparametrization and up to some random hitting time, is equivalent to that of SLEα2. Moreover, a reparametrized SKLE6,−bBMD has the same distribution as SLE6 for BMD domain constant bBMD.",

keywords = "Absorbing Brownian motion, Locality, SLE, Standard slit domain, Stochastic Komatu–Loewner evolution",

author = "Chen, {Zhen Qing} and Masatoshi Fukushima and Hiroyuki Suzuki",

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doi = "10.1016/j.spa.2016.09.006",

language = "English",

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T1 - Stochastic Komatu–Loewner evolutions and SLEs

AU - Chen, Zhen Qing

AU - Fukushima, Masatoshi

AU - Suzuki, Hiroyuki

PY - 2017/6/1

Y1 - 2017/6/1

N2 - A stochastic Komatu–Loewner evolution SKLEα,b has been introduced in Chen and Fukushima (2016) on a standard slit domain determined by certain continuous homogeneous functions α and b. We show that after a suitable reparametrization, SKLEα,b has the same distribution as the chordal Loewner evolution on H driven by a continuous semimartingale. When α is constant, we show that the distribution of SKLEα,b, after a suitable reparametrization and up to some random hitting time, is equivalent to that of SLEα2. Moreover, a reparametrized SKLE6,−bBMD has the same distribution as SLE6 for BMD domain constant bBMD.

AB - A stochastic Komatu–Loewner evolution SKLEα,b has been introduced in Chen and Fukushima (2016) on a standard slit domain determined by certain continuous homogeneous functions α and b. We show that after a suitable reparametrization, SKLEα,b has the same distribution as the chordal Loewner evolution on H driven by a continuous semimartingale. When α is constant, we show that the distribution of SKLEα,b, after a suitable reparametrization and up to some random hitting time, is equivalent to that of SLEα2. Moreover, a reparametrized SKLE6,−bBMD has the same distribution as SLE6 for BMD domain constant bBMD.

KW - Absorbing Brownian motion

KW - Locality

KW - SLE

KW - Standard slit domain

KW - Stochastic Komatu–Loewner evolution

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DO - 10.1016/j.spa.2016.09.006

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SN - 0304-4149

VL - 127

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JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 6

ER -

Stochastic Komatu–Loewner evolutions and SLEs

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Keywords

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