|Ph.D Student||Neuman Eyal|
|Subject||Pathwise Uniqueness of the Stochastic Heat Equations with|
Spatially Inhomogeneous White Noise
|Department||Department of Industrial Engineering and Management||Supervisor||Professor Leonid Mytnik|
|Full Thesis text|
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.