M.Sc Student | Mamin Rustam |
---|---|

Subject | Superprocesse with Infinite Mean |

Department | Department of Applied Mathematics |

Supervisor | Professor Leonid Mytnik |

In this work we prove that for any
dimension *d≥0* and for any *0<γ<1* superprocess defined
on *R*^{d} and corresponding to the Log-Laplace equation

*v _{tt}(t,x)=∆v(t,x)^{γ}(t,x),*

*v(0,x)=f(x)*

is absolutely continuous with respect
to the Lebesgue measure at any fixed time *t>0*.

Our proof is based on properties of
solutions of the Log-Laplace equation. We also prove that when initial datum *v(0,∙)*
is a finite, non-zero measure, then the Log-Laplace equation has a unique,
continuous solution. Moreover this solution continuously depends on initial
data.