4 papers
Functional central limit theorem for superdiffusive SDEs with stable noise
Aleksandar MijatoviÄ, Andrey Pilipenko, Isao Sauzedde
This paper establishes a functional stable central limit theorem for a class of superdiffusive solutions to stochastic differential equations driven by an -stable process.
Brownian paths as loop-decorated SLEs
Nathanaël Berestycki, Isao Sauzedde
We construct an application, which takes as input a simple path and a possibly infinite collection of loops, and outputs a continuous path by adding the loops chronologically to th…
Brownian windings, Stochastic Green's formula and inhomogeneous magnetic impurities
Isao Sauzedde
We give a general Green formula for the planar Brownian motion, which we apply to study the Aharonov--Bohm effect induced by Poisson distributed magnetic impurities on a Brownian e…
Renormalised Amperean Area of Brownian Motions and Symanzik Representation of the 2D Abelian Yang--Mills--Higgs Field
Isao Sauzedde
We construct and study the renormalised Amperean area of a Brownian motion. First studied by W.Werner, the Amperean area is related to Lévy area and stochastic integrals in a way…