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Stochastic Komatu–Loewner evolutions and SLEs

Author

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  • Chen, Zhen-Qing
  • Fukushima, Masatoshi
  • Suzuki, Hiroyuki

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.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:6:p:2068-2087
    DOI: 10.1016/j.spa.2016.09.006
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    Cited by:

    1. Chen, Zhen-Qing & Peng, Jun, 2018. "Markov processes with darning and their approximations," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 3030-3053.
    2. 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.
    3. 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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