Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 545-594 |
| Number of pages | 50 |
| Journal | Stochastic Processes and their Applications |
| Volume | 128 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Feb 2018 |
| Externally published | Yes |
Keywords
- BMD domain constant
- Brownian motion with darning
- Generalized Komatu–Loewner equation for image hulls
- Komatu–Loewner equation for slits
- Locality property
- SDE with homogeneous coefficients
- Stochastic Komatu–Loewner evolution
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Chen, Z. Q., & Fukushima, M. (2018). Stochastic Komatu–Loewner evolutions and BMD domain constant. Stochastic Processes and their Applications, 128(2), 545-594. https://doi.org/10.1016/j.spa.2017.05.007