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Fractional Brownian motion with multivariate time: persistence exponents

  • George Molchan
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Abstract

We consider fractional Brownian motion with D-dimensional time in the domain G(T)=(-T<ti0 if j<d+1). Let P(T) be the probability that the process will not exceed a fixed level in G(T). We show that for large T, logP(T)=(D-dH)logT(1+o(1)) where H is the Hurst parameter of the process

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Cite

BibTeXRIS
BibTeX
@misc{molchan2026fractional,
  title = {{Fractional Brownian motion with multivariate time: persistence exponents}},
  author = {George Molchan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.26680},
  eprint = {2608.26680},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.26680},
}
RIS
TY  - UNPB
TI  - Fractional Brownian motion with multivariate time: persistence exponents
AU  - George Molchan
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2608.26680
UR  - https://arxiv.org/abs/2608.26680
AB  - We consider fractional Brownian motion with D-dimensional time in the domain G(T)=(-T<ti0 if j<d+1). Let P(T) be the probability that the process will not exceed a fixed level in G(T). We show that for large T, logP(T)=(D-dH)logT(1+o(1)) where H is the Hurst parameter of the process
ER  -