Absolute continuity of the super-Brownian motion with infinite mean

Rustam Mamin, Leonid Mytnik

Research output: Contribution to journalArticlepeer-review


In this work, we prove that for any dimension d ≥ 1andanyγ ∈ (0, 1) super-Brownian motion corresponding to the log-Laplace equation (Formula Presented) is absolutely continuous with respect to Lebesgue measure at any fixed time t>0. {St }t≥0 denotes a transition semigroup of a standard Brownian motion. 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.

Original languageEnglish
Pages (from-to)791-810
Number of pages20
JournalBrazilian Journal of Probability and Statistics
Issue number4
StatePublished - 1 Nov 2021


  • Stable branching
  • Superprocesses

All Science Journal Classification (ASJC) codes

  • Statistics and Probability


Dive into the research topics of 'Absolute continuity of the super-Brownian motion with infinite mean'. Together they form a unique fingerprint.

Cite this