|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 Rd and corresponding to the Log-Laplace equation
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.