Work

On Loewner chains driven by semimartingales and complex Bessel-type SDEs

Year: 2024

Type: article

Abstract: 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 SKLEα,b are generated by curves. As another application, motivated by a question of A. Sepúlveda, we show that for α>3/2 and Brownian motion B, the driving function |Bt|α 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 SLEκ, κ<4, in terms of stochastic flow of such SDEs.

Source: The Annals of Applied Probability

DOI: 10.1214/24-aap2091

Authors: Vlad Margarint, Atul Shekhar, Yizheng Yuan

Institutions: University of North Carolina at Charlotte, Tata Institute of Fundamental Research, University of Cambridge

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4405456487

FWCI: 0.653

Cites: 35

Cited by: 1

Related to: 10