ON LOEWNER CHAINS DRIVEN BY SEMIMARTINGALES AND COMPLEX BESSEL-TYPE SDES

• 成果类型: Article
• 署名作者: Margarint, Vlad; Shekhar, Atul; Yuan, Yizheng
• 署名单位: University of North Carolina; University of North Carolina Charlotte; Tata Institute of Fundamental Research (TIFR); University of Cambridge
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2091
• 发表日期: 2024
• 页码: 5258-5286
• 关键词: quantum-gravity; sle; EQUATIONS; energy

摘要

We prove existence (and simpleness) of the trace for both forward and backward Loewner chains under fairly general conditions on semimartingale drivers. As an application, we show that stochastic Komatu-Loewner evolutions SKLE alpha,b are generated by curves. As another application, motivated by a question of A. Sep & uacute;lveda, we show that for alpha > 3/2 and Brownian motion B, the driving function |B-t |(alpha) generates a simple curve for small t. On a related note we also introduce a complex variant of Bessel-type SDEs and prove existence and uniqueness of strong solution. Such SDEs appear naturally while describing the trace of Loewner chains. In particular, we write SLE kappa, kappa <4, in terms of stochastic flow of such SDEs.