Stochastic Loewner Evolution Driven By Lvy Skew Stable Processes |
Posted on:2017-01-30 | Degree:Master | Type:Thesis |
Country:China | Candidate:H N Bian | Full Text:PDF |
GTID:2310330488454528 | Subject:Basic mathematics |
Abstract/Summary: | PDF Full Text Request |
A stochastic Loewner evolution(SLE?for short) is a one-parameter family of random planar growth processes constructed by solving the Loewner equation when the driving function is a one-dimension Brownian motion. This process is intimately connected with scaling limits of percolation clusters. In this thesis we investigate the Loewner differential equation when the driving function is equal to the sum of a onedimension Brownian motion and a Lvy skew stable process. We derive that the derivatives estimates of conformal mappings for the backward flow of the Loewner equation.The pathwise increment estimates of the Lvy skew stable process are obtained. It is proved that the corresponding increasing hull is generated by a curve which is right continuous with left limit. |
Keywords/Search Tags: | SLE, hull, Loewner equation, Brownian motion, Lvy skew stable process |
PDF Full Text Request |
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