TY - JOUR
T1 - Stochastic Komatu–Loewner evolutions and SLEs
AU - Chen, Zhen Qing
AU - Fukushima, Masatoshi
AU - Suzuki, Hiroyuki
N1 - Publisher Copyright:
© 2016 Elsevier B.V.
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
UR - https://www.scopus.com/pages/publications/85008877365
U2 - 10.1016/j.spa.2016.09.006
DO - 10.1016/j.spa.2016.09.006
M3 - Article
AN - SCOPUS:85008877365
SN - 0304-4149
VL - 127
SP - 2068
EP - 2087
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 6
ER -