טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentNeuman Eyal
SubjectPathwise Uniqueness of the Stochastic Heat Equations with
Spatially Inhomogeneous White Noise
DepartmentDepartment of Industrial Engineering and Management
Supervisor Professor Leonid Mytnik
Full Thesis textFull thesis text - English Version


Abstract

We study the solutions of the stochastic heat equation driven by spatially inhomogeneous white noise based on a fractal measure. When the noise coefficient is the square root function, such equations arise as scaling limits of critical branching particle systems which are known as catalytic super Brownian motion. In particular we prove the pathwise uniqueness for solutions of the stochastic heat equation driven by spatially inhomogeneous  if the noise coefficient is Hölder continuous of index γ>1-η/(2(η )) in u. Here η is a constant in the interval (0,1), that defines the spatial regularity of the noise.