Stochastic Komatu–Loewner evolutions and BMD domain constant

Zhen Qing Chen; Masatoshi Fukushima

doi:10.1016/j.spa.2017.05.007

Stochastic Komatu–Loewner evolutions and BMD domain constant

Zhen Qing Chen^*, Masatoshi Fukushima

^*Corresponding author for this work

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

10 Citations (Scopus)

Abstract

For Komatu–Loewner equation on a standard slit domain, we randomize the Jordan arc in a manner similar to that of Schramm (2000) to find the SDEs satisfied by the induced motion ξ(t) on ∂H and the slit motion s(t). The diffusion coefficient α and drift coefficient b of such SDEs are homogeneous functions. Next with solutions of such SDEs, we study the corresponding stochastic Komatu–Loewner evolution, denoted as SKLE_α,b. We introduce a function b_BMD measuring the discrepancy of a standard slit domain from H relative to BMD. We show that SKLE_{6,−b_BMD} enjoys a locality property.

Original language	English
Pages (from-to)	545-594
Number of pages	50
Journal	Stochastic Processes and their Applications
Volume	128
Issue number	2
DOIs	https://doi.org/10.1016/j.spa.2017.05.007
Publication status	Published - Feb 2018
Externally published	Yes

Keywords

BMD domain constant
Brownian motion with darning
Generalized Komatu–Loewner equation for image hulls
Komatu–Loewner equation for slits
Locality property
SDE with homogeneous coefficients
Stochastic Komatu–Loewner evolution

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10.1016/j.spa.2017.05.007

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@article{4634a77d2b314e6fa54a906b0664fc86,

title = "Stochastic Komatu–Loewner evolutions and BMD domain constant",

abstract = "For Komatu–Loewner equation on a standard slit domain, we randomize the Jordan arc in a manner similar to that of Schramm (2000) to find the SDEs satisfied by the induced motion ξ(t) on ∂H and the slit motion s(t). The diffusion coefficient α and drift coefficient b of such SDEs are homogeneous functions. Next with solutions of such SDEs, we study the corresponding stochastic Komatu–Loewner evolution, denoted as SKLEα,b. We introduce a function bBMD measuring the discrepancy of a standard slit domain from H relative to BMD. We show that SKLE6,−bBMD enjoys a locality property.",

keywords = "BMD domain constant, Brownian motion with darning, Generalized Komatu–Loewner equation for image hulls, Komatu–Loewner equation for slits, Locality property, SDE with homogeneous coefficients, Stochastic Komatu–Loewner evolution",

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

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

year = "2018",

month = feb,

doi = "10.1016/j.spa.2017.05.007",

language = "English",

volume = "128",

pages = "545--594",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier B.V.",

number = "2",

}

TY - JOUR

T1 - Stochastic Komatu–Loewner evolutions and BMD domain constant

AU - Chen, Zhen Qing

AU - Fukushima, Masatoshi

PY - 2018/2

Y1 - 2018/2

N2 - For Komatu–Loewner equation on a standard slit domain, we randomize the Jordan arc in a manner similar to that of Schramm (2000) to find the SDEs satisfied by the induced motion ξ(t) on ∂H and the slit motion s(t). The diffusion coefficient α and drift coefficient b of such SDEs are homogeneous functions. Next with solutions of such SDEs, we study the corresponding stochastic Komatu–Loewner evolution, denoted as SKLEα,b. We introduce a function bBMD measuring the discrepancy of a standard slit domain from H relative to BMD. We show that SKLE6,−bBMD enjoys a locality property.

AB - For Komatu–Loewner equation on a standard slit domain, we randomize the Jordan arc in a manner similar to that of Schramm (2000) to find the SDEs satisfied by the induced motion ξ(t) on ∂H and the slit motion s(t). The diffusion coefficient α and drift coefficient b of such SDEs are homogeneous functions. Next with solutions of such SDEs, we study the corresponding stochastic Komatu–Loewner evolution, denoted as SKLEα,b. We introduce a function bBMD measuring the discrepancy of a standard slit domain from H relative to BMD. We show that SKLE6,−bBMD enjoys a locality property.

KW - BMD domain constant

KW - Brownian motion with darning

KW - Generalized Komatu–Loewner equation for image hulls

KW - Komatu–Loewner equation for slits

KW - Locality property

KW - SDE with homogeneous coefficients

KW - Stochastic Komatu–Loewner evolution

UR - http://www.scopus.com/inward/record.url?scp=85021393320&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2017.05.007

DO - 10.1016/j.spa.2017.05.007

M3 - Article

AN - SCOPUS:85021393320

SN - 0304-4149

VL - 128

SP - 545

EP - 594

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 2

ER -

Stochastic Komatu–Loewner evolutions and BMD domain constant

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Keywords

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