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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

Citations:

Zbl 0372.60112
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