Projects per year
Abstract
A simple extension is given of the wellknown conformal invariance of harmonic measure in the plane. This equivalence depends on the interpretation of harmonic measure as an exit distribution of planar Brownian motion, and extends conformal invariance to analytic functions which are not injective, as well as allowing for stopping times more general than exit times. This generalization allow considerations of homotopy and reflection to be applied in order to compute new expressions for exit distributions of various domains, as well as the distribution of Brownian motion at certain other stopping times. An application of these methods is the derivation of a number of infinite sum identities, including the Leibniz formula for π and the values of the Riemann ξ function at even integers.
Original language  English 

Pages (fromto)  597616 
Number of pages  20 
Journal  Annales Academiae Scientiarum Fennicae Mathematica 
Volume  43 
DOIs  
Publication status  Published  1 Jan 2018 
Keywords
 Analytic functions
 Exit distribution
 Harmonic measure
 Planar Brownian motion
Projects
 2 Finished

Planar Brownian motion and complex analysis
Australian Research Council (ARC)
2/01/14 → 11/01/17
Project: Research

New Stochastic Processes with Applications in Finance
Klebaner, F., Buchmann, B. & Hamza, K.
Australian Research Council (ARC), Monash University
31/07/09 → 31/12/13
Project: Research