Singularities of stable super-Brownian motion

2016/08/02 by Paul Balança, Balança, Paul, Leonid Mytnik +1
Economics, Econometrics and Finance · Mathematics · #60G07 #60G17 #60G22 #60G44 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60G07 #msc:60G17 #msc:60G22 #msc:60G44

paper · pdf · doi:10.48550/arxiv.1608.00792

31 pages

arxiv created 2016/08/02 · openalex publication_date 2016/08/02 · arxiv updated 2016/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate in this work the spectrum of singularities of super-Brownian motion with stable branching. The main purpose is to provide a uniform description of the latter in high dimension d≥\tfrac2γ-1, presenting the singularities existing at every time t and characterising as well the set of random times at which singularities of higher order appear. In lower dimensions, we give a partial description of the singularities which complement the recent study of the density by Mytnik and Wachtel.

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