Stochastic Komatu–Loewner evolutions and SLEs

Zhen-Qing Chen, Masatoshi Fukushima and Hiroyuki Suzuki

Stochastic Processes and their Applications, 2017, vol. 127, issue 6, 2068-2087

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: Standard slit domain; Stochastic Komatu–Loewner evolution; SLE; Absorbing Brownian motion; Locality (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:6:p:2068-2087

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DOI: 10.1016/j.spa.2016.09.006

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