Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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BOUNDS FOR EXPONENTIAL MOMENTS OF BESSEL PROCESSES

  • Makasu, Cloud (Departments of Mathematics and Applied Mathematics University of the Western Cape)
  • Received : 2018.10.12
  • Accepted : 2019.02.27
  • Published : 2019.09.30
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Abstract

Let $0<{\alpha}<{\infty}$ be fixed, and let $X=(X_t)_{t{\geq}0}$ be a Bessel process with dimension $0<{\theta}{\leq}1$ starting at $x{\geq}0$. In this paper, it is proved that there are positive constants A and D depending only on ${\theta}$ and ${\alpha}$ such that $$E_x\({\exp}[{\alpha}\;\max_{0{\leq}t{\leq}{\tau}}\;X_t]\){\leq}AE_x\({\exp}[D_{\tau}]\)$$ for any stopping time ${\tau}$ of X. This inequality is also shown to be sharp.

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References

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