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.