On the existence of SLE trace: finite energy drivers and non-constant

• 成果类型: Article
• 署名作者: Friz, Peter K.; Shekhar, Atul
• 署名单位: Indian Statistical Institute; Indian Statistical Institute Bangalore; Technical University of Berlin
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0731-3
• 发表日期: 2017
• 页码: 353-376
• 关键词: loewner curves; CONVERGENCE

摘要

Existence of Loewner trace is revisited. We identify finite energy paths (the skeleton of Wiener measure) as natural class of regular drivers for which we find simple and natural estimates in terms of their (Cameron-Martin) norm. Secondly, now dealing with potentially rough drivers, a representation of the derivative of the (inverse of the) Loewner flow is given in terms of a rough- and then pathwise Follmer integral. Assuming the driver within a class of It-processes, an exponential martingale argument implies existence of trace. In contrast to classical (exact) SLE computations, our arguments are well adapted to perturbations, such as non-constant (assuming for technical reasons) and additional finite-energy drift terms.