Bounds for exponential moments of Bessel processes

摘要

Let 0<α<∞ be fixed, and let X=(Xt)t≥0 be a Bessel process with dimension 0<θ≤1 starting at x≥0. In this paper, it is proved that there are positive constants A and D depending only on θ and α such thatEx(exp[αmax0≤t≤τXt])≤AEx(exp[Dτ])for any stopping time τ of X. This inequality is also shown to be sharp.