טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentMamin Rustam
SubjectSuperprocesse with Infinite Mean
DepartmentDepartment of Applied Mathematics
Supervisor Professor Leonid Mytnik


Abstract

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

vtt(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.