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Chordal Komatu–Loewner equation for a family of continuously growing hulls

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  • Murayama, Takuya

Abstract

In this paper, we discuss the chordal Komatu–Loewner equation on standard slit domains in a manner applicable not just to a simple curve but also a family of continuously growing hulls. Especially a conformally invariant characterization of the Komatu–Loewner evolution is obtained. As an application, we prove a sort of conformal invariance, or locality, of the stochastic Komatu–Loewner evolution SKLE6,−bBMD in a fully general setting, which solves an open problem posed by Chen et al. (2017).

Suggested Citation

  • Murayama, Takuya, 2019. "Chordal Komatu–Loewner equation for a family of continuously growing hulls," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2968-2990.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:8:p:2968-2990
    DOI: 10.1016/j.spa.2018.08.012
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    References listed on IDEAS

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    1. Chen, Zhen-Qing & Fukushima, Masatoshi & Suzuki, Hiroyuki, 2017. "Stochastic Komatu–Loewner evolutions and SLEs," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 2068-2087.
    2. Chen, Zhen-Qing & Fukushima, Masatoshi, 2018. "Stochastic Komatu–Loewner evolutions and BMD domain constant," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 545-594.
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