Abstract
Let R*d(t) be the supremum at time t of a Bessel process with dimension d. For T a stopping time, Burkholder has compared the expectationsof (R*d(T) / √d)p and (√T)p for p>0. Replacing the function xp by exponential functions, we obtain some variant of his results.
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References
D.L. BURKHOLDER "Exit times of Brownian motion, and Hardy spaces" Advances in Math. 26, 182–205 (1977).
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© 2000 Springer-Verlag
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Eisenbaum, N. (2000). Exponential inequalities for bessel processes. In: Azéma, J., Ledoux, M., Émery, M., Yor, M. (eds) Séminaire de Probabilités XXXIV. Lecture Notes in Mathematics, vol 1729. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0103799
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DOI: https://doi.org/10.1007/BFb0103799
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