## Exponential inequalities for Bessel processes.(English)Zbl 0959.60071

Azéma, J. (ed.) et al., Séminaire de Probabilités XXXIV. Berlin: Springer. Lect. Notes Math. 1729, 146-150 (2000).
Let $$R^*_d(t)$$ denote the supremum by time $$t\geq 0$$ of a $$d$$-dimensional Bessel process. D. L. Burkholder [Adv. Math. 26, 182-205 (1977; Zbl 0372.60112)] has compared the expectations of $$(R^*_d(T)/\sqrt d)^p$$ and $$(\sqrt T)^p$$ for $$p> 0$$, where $$T$$ is a stopping time. The author presents some variants of Burkholder’s results for the case where the $$p$$th power is replaced by the exponential function.
For the entire collection see [Zbl 0940.00007].

### MSC:

 60J60 Diffusion processes 60E15 Inequalities; stochastic orderings

Zbl 0372.60112
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