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Boundary behavior and optimal pointwise Hölder exponent of the total local time of (1+β)-stable super-Brownian motion

  • Jieliang Hong
  • Du Yang
  • Junyan Zhang
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Abstract

Let Lx be the total local time of one-dimensional super-Brownian motion with (1+β)-stable branching mechanism, 0<β<1. We prove that {x∈ℝ:Lx>0} is almost surely a bounded open interval (L,R) and that hL(L)=hL(R)=1+2/β almost surely, where hL denotes the pointwise Hölder exponent. Thus the pointwise γ-Hölder condition holds at both endpoints for every γ<1+2/β and fails for every γ>1+2/β. The same conclusions hold under the canonical excursion measure.

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Cite

BibTeXRIS
BibTeX
@misc{hong2026boundary,
  title = {{Boundary behavior and optimal pointwise Hölder exponent of the total local time of $(1+β)$-stable super-Brownian motion}},
  author = {Jieliang Hong and Du Yang and Junyan Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.00690},
  eprint = {2609.00690},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.00690},
}
RIS
TY  - UNPB
TI  - Boundary behavior and optimal pointwise Hölder exponent of the total local time of (1+β)-stable super-Brownian motion
AU  - Jieliang Hong
AU  - Du Yang
AU  - Junyan Zhang
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.00690
UR  - https://arxiv.org/abs/2609.00690
AB  - Let L^x be the total local time of one-dimensional super-Brownian motion with (1+β)-stable branching mechanism, 0<β<1. We prove that {x∈ℝ:L^x>0} is almost surely a bounded open interval (L,R) and that h_L(L)=h_L(R)=1+2/β almost surely, where h_L denotes the pointwise Hölder exponent. Thus the pointwise γ-Hölder condition holds at both endpoints for every γ<1+2/β and fails for every γ>1+2/β. The same conclusions hold under the canonical excursion measure.
ER  -