TY - JOUR
T1 - Stochastic Komatu–Loewner evolutions and BMD domain constant
AU - Chen, Zhen Qing
AU - Fukushima, Masatoshi
N1 - Publisher Copyright:
© 2017 Elsevier B.V.
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 -